Chapter 4: Clustering
I
02/14/2018 Introduction to Data Mining, 2nd Edition ‹#›
What is Cluster Analysis?
Finding groups of objects such that the objects in a group will be similar (or related) to one another and different from (or unrelated to) the objects in other groups
Inter-cluster distances are maximized
Intra-cluster distances are minimized
02/14/2018 Introduction to Data Mining, 2nd Edition ‹#›
Applications of Cluster Analysis
Understanding
Group related documents for browsing, group genes and proteins that have similar functionality, or group stocks with similar price fluctuations
Summarization
Reduce the size of large data sets
Clustering precipitation in Australia
02/14/2018 Introduction to Data Mining, 2nd Edition ‹#›
What is not Cluster Analysis?
Simple segmentation
Dividing students into different registration groups alphabetically, by last name
Results of a query
Groupings are a result of an external specification
Clustering is a grouping of objects based on the data
Supervised classification
Have class label information
Association Analysis
Local vs. global connections
02/14/2018 Introduction to Data Mining, 2nd Edition ‹#›
Notion of a Cluster can be Ambiguous
How many clusters?
Four Clusters
Two Clusters
Six Clusters
02/14/2018 Introduction to Data Mining, 2nd Edition ‹#›
Types of Clusterings
A clustering is a set of clusters
Important distinction between hierarchical and partitional sets of clusters
Partitional Clustering
A division of data objects into non-overlapping subsets (clusters) such that each data object is in exactly one subset
Hierarchical clustering
A set of nested clusters organized as a hierarchical tree
02/14/2018 Introduction to Data Mining, 2nd Edition ‹#›
Partitional Clustering
Original Points
A Partitional Clustering
02/14/2018 Introduction to Data Mining, 2nd Edition ‹#›
Hierarchical Clustering
Traditional Hierarchical Clustering
Non-traditional Hierarchical Clustering
Non-traditional Dendrogram
Traditional Dendrogram
02/14/2018 Introduction to Data Mining, 2nd Edition ‹#›
Types of Clusters
Well-separated clusters
Center-based clusters
Contiguous clusters
Density-based clusters
Property or Conceptual
Described by an Objective Function
02/14/2018 Introduction to Data Mining, 2nd Edition ‹#›
Types of Clusters: Well-Separated
Well-Separated Clusters:
A cluster is a set of points such that any point in a cluster is closer (or more similar) to every other point in the cluster than to any point not ...
Cluster analysis is an unsupervised machine learning technique used to group unlabeled data points into clusters based on similarities. It is useful for applications such as understanding relationships between data points, data summarization, and identifying hidden patterns. The document discusses different types of cluster analysis including partitional clustering which divides data into disjoint clusters and hierarchical clustering which produces nested clusters organized as a tree structure. It also covers various cluster characteristics, algorithms like K-means, and factors that impact cluster analysis results.
The document discusses cluster analysis and various clustering algorithms. It begins with an introduction to cluster analysis, describing what clusters are and some applications of clustering techniques. It then categorizes major clustering methods into partitioning methods, hierarchical methods, density-based methods, and others. Finally, it describes two partitioning algorithms - k-means and k-medoids - in more detail. The k-means algorithm is explained as selecting initial cluster centers, assigning all objects to the closest center, and updating centers repeatedly until convergence.
This document discusses various clustering analysis methods including k-means, k-medoids (PAM), and CLARA. It explains that clustering involves grouping similar objects together without predefined classes. Partitioning methods like k-means and k-medoids (PAM) assign objects to clusters to optimize a criterion function. K-means uses cluster centroids while k-medoids uses actual data points as cluster representatives. PAM is more robust to outliers than k-means but does not scale well to large datasets, so CLARA applies PAM to samples of the data. Examples of clustering applications include market segmentation, land use analysis, and earthquake studies.
This document provides an overview of cluster analysis and clustering algorithms. It defines cluster analysis as grouping objects such that objects within a group are similar to each other and different from objects in other groups. The document discusses different types of clusters, including well-separated, prototype-based, contiguity-based, and density-based clusters. It also covers hierarchical and partitional clustering. Finally, it describes the widely used k-means clustering algorithm and its objective function.
- Hierarchical clustering produces nested clusters organized as a hierarchical tree called a dendrogram. It can be either agglomerative, where each point starts in its own cluster and clusters are merged, or divisive, where all points start in one cluster which is recursively split.
- Common hierarchical clustering algorithms include single linkage (minimum distance), complete linkage (maximum distance), group average, and Ward's method. They differ in how they calculate distance between clusters during merging.
- K-means is a partitional clustering algorithm that divides data into k non-overlapping clusters based on minimizing distance between points and cluster centroids. It is fast but sensitive to initialization and assumes spherical clusters of similar size and density.
Clustering is the process of grouping similar data points together. There are different types of clustering algorithms like k-means clustering, DBSCAN clustering, and self-organizing maps. K-means clustering divides data into k groups by finding cluster centroids. It assigns data points to the nearest centroid and recalculates centroids until clusters stabilize. DBSCAN clustering finds core data points that have many nearby points and groups them into clusters based on density. Self-organizing maps use neural networks to place similar data objects close to each other on a 2D grid based on their similarity to centroid values that are updated during training.
This document provides an introduction to document clustering and clustering algorithms. It discusses how clustering can be used in information retrieval applications like organizing search results and improving search recall. It also covers different types of clustering algorithms like partitioning algorithms (such as K-means) and hierarchical algorithms. Key steps of the K-means and hierarchical agglomerative clustering algorithms are described.
Cluster analysis is an unsupervised machine learning technique used to group unlabeled data points into clusters based on similarities. It is useful for applications such as understanding relationships between data points, data summarization, and identifying hidden patterns. The document discusses different types of cluster analysis including partitional clustering which divides data into disjoint clusters and hierarchical clustering which produces nested clusters organized as a tree structure. It also covers various cluster characteristics, algorithms like K-means, and factors that impact cluster analysis results.
The document discusses cluster analysis and various clustering algorithms. It begins with an introduction to cluster analysis, describing what clusters are and some applications of clustering techniques. It then categorizes major clustering methods into partitioning methods, hierarchical methods, density-based methods, and others. Finally, it describes two partitioning algorithms - k-means and k-medoids - in more detail. The k-means algorithm is explained as selecting initial cluster centers, assigning all objects to the closest center, and updating centers repeatedly until convergence.
This document discusses various clustering analysis methods including k-means, k-medoids (PAM), and CLARA. It explains that clustering involves grouping similar objects together without predefined classes. Partitioning methods like k-means and k-medoids (PAM) assign objects to clusters to optimize a criterion function. K-means uses cluster centroids while k-medoids uses actual data points as cluster representatives. PAM is more robust to outliers than k-means but does not scale well to large datasets, so CLARA applies PAM to samples of the data. Examples of clustering applications include market segmentation, land use analysis, and earthquake studies.
This document provides an overview of cluster analysis and clustering algorithms. It defines cluster analysis as grouping objects such that objects within a group are similar to each other and different from objects in other groups. The document discusses different types of clusters, including well-separated, prototype-based, contiguity-based, and density-based clusters. It also covers hierarchical and partitional clustering. Finally, it describes the widely used k-means clustering algorithm and its objective function.
- Hierarchical clustering produces nested clusters organized as a hierarchical tree called a dendrogram. It can be either agglomerative, where each point starts in its own cluster and clusters are merged, or divisive, where all points start in one cluster which is recursively split.
- Common hierarchical clustering algorithms include single linkage (minimum distance), complete linkage (maximum distance), group average, and Ward's method. They differ in how they calculate distance between clusters during merging.
- K-means is a partitional clustering algorithm that divides data into k non-overlapping clusters based on minimizing distance between points and cluster centroids. It is fast but sensitive to initialization and assumes spherical clusters of similar size and density.
Clustering is the process of grouping similar data points together. There are different types of clustering algorithms like k-means clustering, DBSCAN clustering, and self-organizing maps. K-means clustering divides data into k groups by finding cluster centroids. It assigns data points to the nearest centroid and recalculates centroids until clusters stabilize. DBSCAN clustering finds core data points that have many nearby points and groups them into clusters based on density. Self-organizing maps use neural networks to place similar data objects close to each other on a 2D grid based on their similarity to centroid values that are updated during training.
This document provides an introduction to document clustering and clustering algorithms. It discusses how clustering can be used in information retrieval applications like organizing search results and improving search recall. It also covers different types of clustering algorithms like partitioning algorithms (such as K-means) and hierarchical algorithms. Key steps of the K-means and hierarchical agglomerative clustering algorithms are described.
The document provides an overview of different clustering methods including partitioning methods like k-means and k-medoids, hierarchical methods like agglomerative and divisive, and density-based methods like DBSCAN and OPTICS. It discusses the basic concepts of clustering, requirements for effective clustering like scalability and ability to handle different data types and shapes. It also summarizes clustering algorithms like BIRCH that aim to improve scalability for large datasets.
This document introduces data exploration and reduction techniques in XLMiner, including principal component analysis and cluster analysis. Principal component analysis transforms correlated variables into uncorrelated principal components to reduce data size while maintaining variability. Cluster analysis assigns objects to clusters to group similar objects together and different objects apart. The document demonstrates how to perform k-means clustering and hierarchical clustering in XLMiner.
This document introduces data exploration and reduction techniques in XLMiner, including principal component analysis and cluster analysis. Principal component analysis transforms correlated variables into uncorrelated principal components to reduce data size while maintaining variability. Cluster analysis assigns objects to clusters to group similar objects together and different objects apart. The document demonstrates how to perform k-means clustering and hierarchical clustering in XLMiner.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Cluster analysis is used to group similar objects together and separate dissimilar objects. It has applications in understanding data patterns and reducing large datasets. The main types are partitional which divides data into non-overlapping subsets, and hierarchical which arranges clusters in a tree structure. Popular clustering algorithms include k-means, hierarchical clustering, and graph-based clustering. K-means clustering assigns data points to centroids to minimize distance within clusters. Hierarchical clustering creates nested clusters and can be visualized using dendrograms. Both have benefits and limitations depending on the dataset.
Cluster analysis is used to group similar objects together and separate dissimilar objects. It has applications in understanding data patterns and reducing large datasets. The main types are partitional which divides data into non-overlapping subsets, and hierarchical which arranges clusters in a tree structure. Popular clustering algorithms include k-means, hierarchical clustering, and graph-based clustering. K-means partitions data into k clusters by minimizing distances between points and cluster centroids, but requires specifying k and is sensitive to initial centroid positions. Hierarchical clustering creates nested clusters without needing to specify the number of clusters, but has higher computational costs.
Cluster analysis is used to group similar objects together and separate dissimilar objects. It has applications in understanding data patterns and reducing large datasets. The main types are partitional which divides data into non-overlapping subsets, and hierarchical which arranges clusters in a tree structure. Popular clustering algorithms include k-means, hierarchical clustering, and graph-based clustering. K-means partitions data into k clusters by minimizing distances between points and cluster centroids, but requires specifying k and is sensitive to initial centroid positions. Hierarchical clustering creates nested clusters without needing to specify the number of clusters, but has higher computational costs.
Data Mining Primitives, Languages & SystemsNiloy Sikder
The document summarizes the key primitives and concepts in data mining. It discusses the main primitives as task-relevant data, knowledge types to be mined, and background knowledge. It describes various data mining techniques including data selection, grouping, characterization, discrimination, associations and correlations. It also discusses classification methods and prediction. Finally, it covers data mining system architectures and languages such as DMQL and OLE DB.
This document provides an introduction and overview of document clustering techniques in information retrieval. It discusses motivations for clustering documents, such as improving search recall and organizing search results. It covers common clustering algorithms like K-means and hierarchical clustering, how they work, and considerations like choosing the number of clusters. The document uses examples and diagrams to illustrate clustering concepts and algorithms.
This document provides an introduction and overview of document clustering techniques in information retrieval. It discusses motivations for clustering documents, such as improving search recall and organizing search results. It covers common clustering algorithms like K-means and hierarchical clustering, how they work, and considerations like choosing the number of clusters. The document uses examples and diagrams to illustrate clustering concepts and algorithms.
This document provides an introduction and overview of document clustering techniques in information retrieval. It discusses motivations for clustering documents, such as improving search recall and organizing search results. It covers common clustering algorithms like K-means and hierarchical clustering, how they work, and considerations like choosing the number of clusters. The document uses examples and diagrams to illustrate clustering concepts and algorithms.
This document provides an introduction and overview of document clustering techniques in information retrieval. It discusses motivations for clustering documents, different document representations, evaluation criteria, and clustering algorithms including partitional algorithms like K-means and hierarchical algorithms. It provides examples and discusses issues like determining the optimal number of clusters to generate. The overall summary is that document clustering groups similar documents together to help with tasks like document navigation, improving search recall, and organizing search results.
This document provides an overview of hierarchical clustering methods. It discusses agglomerative hierarchical clustering methods like AGNES that start by treating each object as a separate cluster and merge them into larger clusters. It also discusses divisive hierarchical clustering methods like DIANA that start with all objects in one cluster and split them into smaller clusters. A dendrogram is used to visualize the nested clustering formed at different levels in the hierarchical clustering tree. The document also discusses different measures for calculating the distance between clusters during the merging or splitting process.
This document provides an overview of supervised and unsupervised learning, with a focus on clustering as an unsupervised learning technique. It describes the basic concepts of clustering, including how clustering groups similar data points together without labeled categories. It then covers two main clustering algorithms - k-means, a partitional clustering method, and hierarchical clustering. It discusses aspects like cluster representation, distance functions, strengths and weaknesses of different approaches. The document aims to introduce clustering and compare it with supervised learning.
This document summarizes a presentation on cluster analysis given by Tekendra Nath Yogi. It defines cluster analysis and describes several clustering methods and algorithms, including k-means clustering. It also discusses applications of cluster analysis in fields like business intelligence, image recognition, web search, and biology. Requirements for effective clustering algorithms are outlined.
Clustering is an unsupervised machine learning technique used to group unlabeled data points. There are two main approaches: hierarchical clustering and partitioning clustering. Partitioning clustering algorithms like k-means and k-medoids attempt to partition data into k clusters by optimizing a criterion function. Hierarchical clustering creates nested clusters by merging or splitting clusters. Examples of hierarchical algorithms include agglomerative clustering, which builds clusters from bottom-up, and divisive clustering, which separates clusters from top-down. Clustering can group both numerical and categorical data.
This document compares hierarchical and non-hierarchical clustering algorithms. It summarizes four clustering algorithms: K-Means, K-Medoids, Farthest First Clustering (hierarchical algorithms), and DBSCAN (non-hierarchical algorithm). It describes the methodology of each algorithm and provides pseudocode. It also describes the datasets used to evaluate the performance of the algorithms and the evaluation metrics. The goal is to compare the performance of the clustering methods on different datasets.
Cluster analysis is an unsupervised machine learning technique used to group unlabeled data points into clusters based on similarities. It involves finding groups of objects such that objects within a cluster are more similar to each other than objects in different clusters. The key goals of cluster analysis are to maximize intra-cluster similarity while minimizing inter-cluster similarity. Common applications of cluster analysis include market segmentation, document classification, and identifying homogeneous groups in biological data.
The document discusses hierarchical clustering methods. It explains that hierarchical clustering builds nested clusters by merging or splitting them based on their distance. Agglomerative hierarchical clustering (AGNES) iteratively merges the closest clusters, while divisive hierarchical clustering (DIANA) iteratively splits clusters. Dendograms are used to visualize how clusters are merged or split at different levels of the hierarchy. The document also discusses different methods for calculating the distance between clusters, such as single, complete, and average linkage.
1. The ALIVE status of each SEX. (SEX needs to be integrated into th.docxketurahhazelhurst
1. The ALIVE status of each SEX. (SEX needs to be integrated into the only Male, Female, ND, and Other) (bar comparison chart, pie comparison chart)
2. How many Male, Female, ND, and Other are there in each ALIGN. (Bar comparison chart)
3. How many red-haired heroes do Marvel and DC have?
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1. Some potentially pathogenic bacteria and fungi, including strains.docxketurahhazelhurst
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2. Human immunodeficiency virus (HIV) preferentially destroys CD4+ cells. Specifically, what effect does this have on antibody and cell-mediated immunity?
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The document provides an overview of different clustering methods including partitioning methods like k-means and k-medoids, hierarchical methods like agglomerative and divisive, and density-based methods like DBSCAN and OPTICS. It discusses the basic concepts of clustering, requirements for effective clustering like scalability and ability to handle different data types and shapes. It also summarizes clustering algorithms like BIRCH that aim to improve scalability for large datasets.
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Cluster analysis is used to group similar objects together and separate dissimilar objects. It has applications in understanding data patterns and reducing large datasets. The main types are partitional which divides data into non-overlapping subsets, and hierarchical which arranges clusters in a tree structure. Popular clustering algorithms include k-means, hierarchical clustering, and graph-based clustering. K-means clustering assigns data points to centroids to minimize distance within clusters. Hierarchical clustering creates nested clusters and can be visualized using dendrograms. Both have benefits and limitations depending on the dataset.
Cluster analysis is used to group similar objects together and separate dissimilar objects. It has applications in understanding data patterns and reducing large datasets. The main types are partitional which divides data into non-overlapping subsets, and hierarchical which arranges clusters in a tree structure. Popular clustering algorithms include k-means, hierarchical clustering, and graph-based clustering. K-means partitions data into k clusters by minimizing distances between points and cluster centroids, but requires specifying k and is sensitive to initial centroid positions. Hierarchical clustering creates nested clusters without needing to specify the number of clusters, but has higher computational costs.
Cluster analysis is used to group similar objects together and separate dissimilar objects. It has applications in understanding data patterns and reducing large datasets. The main types are partitional which divides data into non-overlapping subsets, and hierarchical which arranges clusters in a tree structure. Popular clustering algorithms include k-means, hierarchical clustering, and graph-based clustering. K-means partitions data into k clusters by minimizing distances between points and cluster centroids, but requires specifying k and is sensitive to initial centroid positions. Hierarchical clustering creates nested clusters without needing to specify the number of clusters, but has higher computational costs.
Data Mining Primitives, Languages & SystemsNiloy Sikder
The document summarizes the key primitives and concepts in data mining. It discusses the main primitives as task-relevant data, knowledge types to be mined, and background knowledge. It describes various data mining techniques including data selection, grouping, characterization, discrimination, associations and correlations. It also discusses classification methods and prediction. Finally, it covers data mining system architectures and languages such as DMQL and OLE DB.
This document provides an introduction and overview of document clustering techniques in information retrieval. It discusses motivations for clustering documents, such as improving search recall and organizing search results. It covers common clustering algorithms like K-means and hierarchical clustering, how they work, and considerations like choosing the number of clusters. The document uses examples and diagrams to illustrate clustering concepts and algorithms.
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This document provides an introduction and overview of document clustering techniques in information retrieval. It discusses motivations for clustering documents, such as improving search recall and organizing search results. It covers common clustering algorithms like K-means and hierarchical clustering, how they work, and considerations like choosing the number of clusters. The document uses examples and diagrams to illustrate clustering concepts and algorithms.
This document provides an introduction and overview of document clustering techniques in information retrieval. It discusses motivations for clustering documents, different document representations, evaluation criteria, and clustering algorithms including partitional algorithms like K-means and hierarchical algorithms. It provides examples and discusses issues like determining the optimal number of clusters to generate. The overall summary is that document clustering groups similar documents together to help with tasks like document navigation, improving search recall, and organizing search results.
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This document summarizes a presentation on cluster analysis given by Tekendra Nath Yogi. It defines cluster analysis and describes several clustering methods and algorithms, including k-means clustering. It also discusses applications of cluster analysis in fields like business intelligence, image recognition, web search, and biology. Requirements for effective clustering algorithms are outlined.
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3. Provide your own summary of the film, using psychological terms and concepts that you have learned in class and from your textbook. State clearly the psychological disorder you have seen portrayed in the film you have chosen, using DSM criteria/language. You should explain the psychological disorder portrayed in the movie. Determine and evaluate if the disorder identified in the film is accurate according to your textbook and other resource materials. Provide evidence using actual behaviors seen in the film. Is the depiction of the psychological disorder in the film accurate or not? Give evidence to support your claims using observable behaviors from the movie.
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7. Be sure to use APA format using the latest edition of the APA Manual (7th edition).
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National Academies of Sciences, Engineering, and Medicine
) defined patient-centered care as: "Providing care that is respectful of and responsive to individual patient preferences, needs, and values, and ensuring that patient values guide all clinical decisions.”[1] While this definition clearly emphasizes the importance of a patient’s perspective in the context of clinical care delivery, it does not allow managers to focus on the actual “person” inside the institutional role of the patient.
In the same sense that a person who is incarcerated in a prison may receive extremely humane treatment, the “person” is still defined into the role of an “inmate,” and as such cannot, by definition, be granted the same rights and privileges as a non-institutionalized member of the civil order enjoys. In other words, I may be placed in a cell with great empathy and understanding of my preferences, needs, and values, but I am still being locked-up in jail.
No one is suggesting that being admitted into a jail cell is the same as being admitted into a hospital bed. There are many obvious differences between the two, including the basic purpose of the two institutions.
But while much is different, what is the same is how a pre-existing set of structured behaviors and processes are used to firmly, and without asking or negotiating, radically transform a “regular” person into a defined role of a “patient” that then can be diagnosed, treated, and discharged back into the world once the patient has finished their “time” in the “system.”
While patient-centered care emphasizes the value of increased sensitivity to a patient’s preferences, needs, and values, what we want to focus on is how decisions made by healthcare leaders affect the actual experience of a person receiving that care.
So with the "real person" in mind, this week's question is:
What can healthcare leaders do in improve the actual personal experience that "real people" go through as our "patients?"
(Be sure to develop your answers AFTER you review the definition and roles of "Leadership" in the readings for this week).
[1] Institute on Medicine, Crossing the Quality Chasm: A New Health System for the 21st Century, March, 2001
2. Health Information Technonogy - PPP Discussion
The board has created an innovation fund designed to foster improved quality, increased access, or reduced costs in healthcare delivery. Select a health information technology related to genomics, precision medicine, or diagnostics that you would propose to be funded for implementation. Prepare a PowerPoint presentation that describes the selected health information technology, what it does, why it would be beneficial, and what risks may be involved. Please note, this activity is weighted 5% toward the final grade. The PowerPoint should be no more than 5-6 slides with the presenter's notes. Follow the APA format.
.
1. The Documentary Hypothesis holds that the Pentateuch has a number.docxketurahhazelhurst
1. The Documentary Hypothesis holds that the Pentateuch has a number of underlying documents (alt., sources) that were ultimately gathered and sewn into the Pentateuch as we now have it. The method of separating those underlying documents is called source criticism. Please perform a source-critical analysis of Gen 1-3. In so doing, please identify the significant features that distinguish each underlying document. Note: There are many such features.
2. Why are covenants important in the Bible? What do they accomplish? Are they all the same, whether in structure or outlook? Do the different writers view them differently? What does the ancient Near Eastern background to the biblical covenant contribute to our understanding?
3. Dt 6:4 used to be translated
“Hear, O Israel: The LORD [YHWH] our God, the LORD [YHWH] is one.”
Currently, we translate
“Hear, O Israel: The LORD [YHWH] is our God, the LORD [YHWH] alone.”
In all likelihood, the second translation is grammatically preferable. What is the interpretive difference between “one” and “alone”? Is it significant? How, if at all, does this verse relate to the First Commandment? How does this verse relate to Gen 1:26, 3:22, and 11:7? How does this verse relate to the variant non-MT variant in Dt 32:8-9 (as reproduced in HarperCollins)? Why is any of this important?
Be sure to provide a careful, well-written essay which gives ample biblical examples (proof texts) to support the point(s) you wish to make.
.
1. Search the internet and learn about the cases of nurses Julie.docxketurahhazelhurst
1. Search the internet and learn about the cases of nurses Julie Thao and Kimberly Hiatt.
2. List and discuss lessons that you and all healthcare professionals can learn from these two cases.
3. Describe how the principle of beneficence and the virtue of benevolence could be applied to these cases. Do you think the hospital adminstrators handled the situations legally and ethically?
4. In addition to benevolence, which other virtues exhibited by their colleagues might have helped Thao and Hiatt?
5. Discuss personal virtues that might be helpful to second victims themselves to navigate the grieving process.
Scholarly article, APA format, and no grammar error
.
1. Search the internet and learn about the cases of nurses Julie Tha.docxketurahhazelhurst
1. Search the internet and learn about the cases of nurses Julie Thao and Kimberly Hiatt.
2. List and discuss lessons that you and all healthcare professionals can learn from these two cases.
3. Describe how the principle of beneficence and the virtue of benevolence could be applied to these cases. Do you think the hospital adminstrators handled the situations legally and ethically?
4. In addition to benevolence, which other virtues exhibited by their colleagues might have helped Thao and Hiatt?
5. Discuss personal virtues that might be helpful to second victims themselves to navigate the grieving process.
use reference and scholarly nursing article.
.
1. Review the three articles about Inflation that are found below th.docxketurahhazelhurst
1. Review the three articles about Inflation that are found below this.
Globalization and Inflatio
n
Drivers of Inflation
Inflation
and Unemploymen
t
2. Locate two JOURNAL articles which discuss this topic further. You need to focus on the Abstract, Introduction, Results, and Conclusion. For our purposes, you are not expected to fully understand the Data and Methodology.
3. Summarize these journal articles. Please use your own words. No copy-and-paste. Cite your sources.
4.The replies are due by the deadline specified in the Course Schedule.
Please post (in APA format) your article citation.
.
1. Review the following request from a customerWe have a ne.docxketurahhazelhurst
1. Review the following request from a customer:
We have a need to replace the aging Signage Application. This application is housed in District 4 and serves the district as well as two other districts. We would like a new application that can be used statewide to track all information related to road signs.
The current system is old and doesn’t do most of what we need it to.
The current system has a whole bunch of reports, but no way for the user to update them by themselves without getting IT involved.
We also can’t create our own reports, on-demand, when we need to. Currently, data is entered into the application manually by Administrative Staff, but in the future, we would like to be able to take a picture of the road sign using a phone app, and have it automagically populate the database with geospatial location and other information. We thought about having a Smart Watch interface, but we don’t need that. Also, the current method does not have any way to manage the quality of the data that is entered, so there is a lot of garbage information there. There is no way to centrally manage security access, with the existing application. We want to get real time alerts when a sign gets knocked over in an accident and have a dashboard that shows where signs have been knocked over across the state. This is kind of important, but not super-critical. We need to store location information, types of signs, when a new sign is installed, who installed it, etc. We plan to provide the phone app to drivers in each district who will drive around, take pictures of the signs, and upload them to the database at the end of each day, or in realtime, if a data connection is available.
Back in Central Office, reviewers will review the sign information and validate it. A report will be printed every month with the results and a map. There are probably other things, but we can’t think of anything else right now.
2. List the main goal(s) of this request
3. Write all the user stories you see (include value statements and acceptance criteria, if possible)
4. Prioritize the user stories as
a. Critical
b. Important
c. Useful
d. Out of Scope
5. Are the user stories sufficiently detailed? If not, what steps would you take to split them/further define them?
6. What are the known Data Entities?
7. Is there an implied business process? Draw an activity diagram or a flow chart of it
8. Who are the actors/roles?
9. What questions would you ask of the stakeholders to get more information?
10. What technology should be used to implement the solution?
11. What would you do next as the assigned Business Analyst working on an Agile team?
.
1. Research risk assessment approaches.2. Create an outline .docxketurahhazelhurst
1. Research risk assessment approaches.
2. Create an outline for a basic qualitative risk assessment plan.
3. Write an introduction to the plan explaining its purpose and importance.
4. Define the scope and boundaries for the risk assessment.
5. Identify data center assets and activities to be assessed.
6. Identify relevant threats and vulnerabilities. Include those listed in the scenario and add to the list if needed.
7. Identify relevant types of controls to be assessed.
8. Identify the key roles and responsibilities of individuals and departments within the organization as they pertain to risk assessments.
9. Develop a proposed schedule for the risk assessment process.
10. Complete the draft risk assessment plan detailing the information above. Risk assessment plans often include tables, but you choose the best format to present the material. Format the bulk of the plan similar to a professional business report and cite any sources you used.
.
1. Research has narrowed the thousands of leadership behaviors into .docxketurahhazelhurst
1. Research has narrowed the thousands of leadership behaviors into two primary dimensions. Please list and discuss these two behaviors.
2. Distinguish between charismatic, transformational, and authentic leadership. Could an individual display all three types of leadership?
.
1. Research Topic Super Computer Data MiningThe aim of this.docxketurahhazelhurst
1. Research Topic: Super Computer Data Mining
The aim of this project is to produce a super-computing data mining resource for use by the UK academic community which utilizes a number of advanced machine learning and statistical algorithms for large datasets. In particular, a number of evolutionary computing-based algorithms and the ensemble machine approach will be used to exploit the large-scale parallelism possible in super-computing. This purpose is embodied in the following objectives:
1. to develop a massively parallel approach for commonly used statistical and machine learning techniques for exploratory data analysis
1. to develop a massively parallel approach to the use of evolutionary computing techniques for feature creation and selection
1. to develop a massively parallel approach to the use of evolutionary computing techniques for data modelling
1. to develop a massively parallel approach to the use of ensemble machines for data modelling consisting of many well-known machine learning algorithms;
1. to develop an appropriate super-computing infra-structure to support the use of such advanced machine learning techniques with large datasets.
Research Needs:
Problem definition – In the first phase problem definition is listed i.e. business aims and objectives are determined taking into consideration certain factors like the current background and future prospective.
Data exploration – Required data is collected and explored using various statistical methods along with identification of underlying problems.
Data preparation – The data is prepared for modeling by cleansing and formatting the raw data in the desired way. The meaning of data is not changed while preparing.
Modeling – In this phase the data model is created by applying certain mathematical functions and modeling techniques. After the model is created it goes through validation and verification.
Evaluation – After the model is created, it is evaluated by a team of experts to check whether it satisfies business objectives or not.
Deployment – After evaluation, the model is deployed and further plans are made for its maintenance. A properly organized report is prepared with the summary of the work done.
Research paper Policy
· APA format
. https://apastyle.apa.org/
. https://owl.purdue.edu/owl/research_and_citation/apa_style/apa_formatting_and_style_guide/general_format.html
· Min number of pages are 15 pages
· Must have
. Contents with page numbers
. Abstract
. Introduction
. The problem
4. Are there any sub-problems?
4. Is there any issue need to be present concerning the problem?
. The solutions
5. Steps of the solutions
. Compare the solution to other solution
. Any suggestion to improve the solution
. Conclusion
. References
· Missing one of the above will result -5/30 of the research paper
· Paper does not stick to the APA will result in 0 in the research paper
· Submission
. you have multiple submission to check you safe assignments
. The percentage accepted is 1%.
1. Research and then describe about The Coca-Cola Company primary bu.docxketurahhazelhurst
1. Research and then describe about The Coca-Cola Company primary business activities. Include: Minimum 7 Pages. Excluding reference page
2.
A. A brief historical summary,
B. A list of competitors,
C. The company's position within the industry,
D. Recent developments within the company/industry,
E. Future direction, and
F. Other items of significance to your corporation.
3. Include information from a variety of resources. For example:
A. Consult the Form 10-K filed with the SEC.
B. Review the Annual Report and especially the Letter to Shareholders
C. Explore the corporate website.
D. Select at least two significant news items from recent business periodicals
The report should be well written with cover page, introduction, the body of the paper (with appropriate subheadings), conclusion, and reference page.
.
1. Prepare a risk management plan for the project of finding a job a.docxketurahhazelhurst
1. Prepare a risk management plan for the project of finding a job after graduation.
and
2. Develop a reward system for motivating IPT members to do their jobs more conscientiously and to take on more responsibility.
[The assignment should be at least 400 words minimum and in APA format (including Times New Roman with font size 12 and double spaced), and attached as a WORD file.]
Plagiarism free
.
1. Please define the term social class. How is it usually measured .docxketurahhazelhurst
1. Please define the term social class. How is it usually measured? What are some ways that social class is affecting health outcomes for people who become ill with COVID-19?
2. What is the CARES Act? Has it been enough? What has happened to people's ability to pay their bills since it expired?
3. As things stand now, data is showing higher COVID-19 related mortality rates for African Americans. Given what you know from the textbook and from the attached articles, what are some explanations for the disparity?
4. What is environmental racism (injustice)? How does environmental racism put some populations at higher risk for severe medical complications than others? (Vice article)
https://www.theatlantic.com/ideas/archive/2020/07/600-week-buys-freedom-fear/613972/
https://www.vox.com/2020/4/10/21207520/coronavirus-deaths-economy-layoffs-inequality-covid-pandemic
https://www.vice.com/en_us/article/pke94n/cancer-alley-has-some-of-the-highest-coronavirus-death-rates-in-the-country
https://www.theguardian.com/us-news/2020/apr/12/coronavirus-us-deep-south-poverty-race-perfect-storm
.
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...PECB
Denis is a dynamic and results-driven Chief Information Officer (CIO) with a distinguished career spanning information systems analysis and technical project management. With a proven track record of spearheading the design and delivery of cutting-edge Information Management solutions, he has consistently elevated business operations, streamlined reporting functions, and maximized process efficiency.
Certified as an ISO/IEC 27001: Information Security Management Systems (ISMS) Lead Implementer, Data Protection Officer, and Cyber Risks Analyst, Denis brings a heightened focus on data security, privacy, and cyber resilience to every endeavor.
His expertise extends across a diverse spectrum of reporting, database, and web development applications, underpinned by an exceptional grasp of data storage and virtualization technologies. His proficiency in application testing, database administration, and data cleansing ensures seamless execution of complex projects.
What sets Denis apart is his comprehensive understanding of Business and Systems Analysis technologies, honed through involvement in all phases of the Software Development Lifecycle (SDLC). From meticulous requirements gathering to precise analysis, innovative design, rigorous development, thorough testing, and successful implementation, he has consistently delivered exceptional results.
Throughout his career, he has taken on multifaceted roles, from leading technical project management teams to owning solutions that drive operational excellence. His conscientious and proactive approach is unwavering, whether he is working independently or collaboratively within a team. His ability to connect with colleagues on a personal level underscores his commitment to fostering a harmonious and productive workplace environment.
Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
-------------------------------------------------------------------------------
Find out more about ISO training and certification services
Training: ISO/IEC 27001 Information Security Management System - EN | PECB
ISO/IEC 42001 Artificial Intelligence Management System - EN | PECB
General Data Protection Regulation (GDPR) - Training Courses - EN | PECB
Webinars: https://pecb.com/webinars
Article: https://pecb.com/article
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For more information about PECB:
Website: https://pecb.com/
LinkedIn: https://www.linkedin.com/company/pecb/
Facebook: https://www.facebook.com/PECBInternational/
Slideshare: http://www.slideshare.net/PECBCERTIFICATION
This presentation was provided by Steph Pollock of The American Psychological Association’s Journals Program, and Damita Snow, of The American Society of Civil Engineers (ASCE), for the initial session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session One: 'Setting Expectations: a DEIA Primer,' was held June 6, 2024.
How to Manage Your Lost Opportunities in Odoo 17 CRMCeline George
Odoo 17 CRM allows us to track why we lose sales opportunities with "Lost Reasons." This helps analyze our sales process and identify areas for improvement. Here's how to configure lost reasons in Odoo 17 CRM
A Strategic Approach: GenAI in EducationPeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Introduction to AI for Nonprofits with Tapp NetworkTechSoup
Dive into the world of AI! Experts Jon Hill and Tareq Monaur will guide you through AI's role in enhancing nonprofit websites and basic marketing strategies, making it easy to understand and apply.
বাংলাদেশের অর্থনৈতিক সমীক্ষা ২০২৪ [Bangladesh Economic Review 2024 Bangla.pdf] কম্পিউটার , ট্যাব ও স্মার্ট ফোন ভার্সন সহ সম্পূর্ণ বাংলা ই-বুক বা pdf বই " সুচিপত্র ...বুকমার্ক মেনু 🔖 ও হাইপার লিংক মেনু 📝👆 যুক্ত ..
আমাদের সবার জন্য খুব খুব গুরুত্বপূর্ণ একটি বই ..বিসিএস, ব্যাংক, ইউনিভার্সিটি ভর্তি ও যে কোন প্রতিযোগিতা মূলক পরীক্ষার জন্য এর খুব ইম্পরট্যান্ট একটি বিষয় ...তাছাড়া বাংলাদেশের সাম্প্রতিক যে কোন ডাটা বা তথ্য এই বইতে পাবেন ...
তাই একজন নাগরিক হিসাবে এই তথ্য গুলো আপনার জানা প্রয়োজন ...।
বিসিএস ও ব্যাংক এর লিখিত পরীক্ষা ...+এছাড়া মাধ্যমিক ও উচ্চমাধ্যমিকের স্টুডেন্টদের জন্য অনেক কাজে আসবে ...
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...Dr. Vinod Kumar Kanvaria
Exploiting Artificial Intelligence for Empowering Researchers and Faculty,
International FDP on Fundamentals of Research in Social Sciences
at Integral University, Lucknow, 06.06.2024
By Dr. Vinod Kumar Kanvaria
it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
1. Chapter 4: Clustering
I
02/14/2018 Introduction to Data Mining, 2nd Edition
‹#›
What is Cluster Analysis?
Finding groups of objects such that the objects in a group will
be similar (or related) to one another and different from (or
unrelated to) the objects in other groups
2. Inter-cluster distances are maximized
Intra-cluster distances are minimized
02/14/2018 Introduction to Data Mining, 2nd Edition
‹#›
Applications of Cluster Analysis
Understanding
Group related documents for browsing, group genes and
proteins that have similar functionality, or group stocks with
similar price fluctuations
Summarization
Reduce the size of large data sets
3. Clustering precipitation in Australia
02/14/2018 Introduction to Data Mining, 2nd Edition
‹#›
What is not Cluster Analysis?
Simple segmentation
Dividing students into different registration groups
alphabetically, by last name
Results of a query
Groupings are a result of an external specification
Clustering is a grouping of objects based on the data
Supervised classification
Have class label information
Association Analysis
Local vs. global connections
02/14/2018 Introduction to Data Mining, 2nd Edition
‹#›
Notion of a Cluster can be Ambiguous
6. Six Clusters
02/14/2018 Introduction to Data Mining, 2nd Edition
‹#›
Types of Clusterings
A clustering is a set of clusters
Important distinction between hierarchical and partitional sets
of clusters
Partitional Clustering
A division of data objects into non-overlapping subsets
(clusters) such that each data object is in exactly one subset
Hierarchical clustering
A set of nested clusters organized as a hierarchical tree
02/14/2018 Introduction to Data Mining, 2nd Edition
‹#›
Partitional Clustering
7. Original Points
A Partitional Clustering
02/14/2018 Introduction to Data Mining, 2nd Edition
‹#›
Hierarchical Clustering
Traditional Hierarchical Clustering
Non-traditional Hierarchical Clustering
Non-traditional Dendrogram
Traditional Dendrogram
02/14/2018 Introduction to Data Mining, 2nd Edition
8. ‹#›
Types of Clusters
Well-separated clusters
Center-based clusters
Contiguous clusters
Density-based clusters
Property or Conceptual
Described by an Objective Function
02/14/2018 Introduction to Data Mining, 2nd Edition
‹#›
Types of Clusters: Well-Separated
Well-Separated Clusters:
A cluster is a set of points such that any point in a cluster is
closer (or more similar) to every other point in the cluster than
to any point not in the cluster.
3 well-separated clusters
02/14/2018 Introduction to Data Mining, 2nd Edition
‹#›
9. Types of Clusters: Center-Based
Center-based
A cluster is a set of objects such that an object in a cluster is
closer to the “center” of a cluster, than to the center of any
other cluster
The center of a cluster is a centroid.
The average of all the points in the cluster is a medoid
4 center-based clusters
02/14/2018 Introduction to Data Mining, 2nd Edition
‹#›
Types of Clusters: Contiguity-Based
Contiguous Cluster (Nearest neighbor or Transitive)
A point in a cluster is closer (or more similar) to one or more
other points in the cluster than to any point not in the cluster.
8 contiguous clusters
10. 02/14/2018 Introduction to Data Mining, 2nd Edition
‹#›
Types of Clusters: Density-Based
Density-based
A cluster is a dense region of points, which is separated by low-
density regions, from other regions of high density.
Used when the clusters are irregular or intertwined, and when
noise and outliers are present.
6 density-based clusters
02/14/2018 Introduction to Data Mining, 2nd Edition
‹#›
Types of Clusters: Conceptual Clusters
Shared Property or Conceptual Clusters
Finds clusters that share some common property or represent a
particular concept.
.
2 Overlapping Circles
11. 02/14/2018 Introduction to Data Mining, 2nd Edition
‹#›
Types of Clusters: Objective Function
Clusters Defined by an Objective Function
Finds clusters that minimize or maximize an objective function.
Enumerate all possible ways of dividing the points into clusters
and evaluate the `goodness' of each potential set of clusters by
using the given objective function. (NP Hard)
Can have global or local objectives.
Hierarchical clustering algorithms typically have local
objectives
Partitional algorithms typically have global objectives
A variation of the global objective function approach is to fit
the data to a parameterized model.
Parameters for the model are determined from the data.
Mixture models assume that the data is a ‘mixture' of a number
of statistical distributions.
02/14/2018 Introduction to Data Mining, 2nd Edition
‹#›
Characteristics of the Input Data Are Important
Type of proximity or density measure
Central to clustering
Depends on data and application
Data characteristics that affect proximity and/or density are
Dimensionality
Sparseness
Attribute type
Special relationships in the data
12. For example, autocorrelation
Distribution of the data
Noise and Outliers
Often interfere with the operation of the clustering algorithm
02/14/2018 Introduction to Data Mining, 2nd Edition
‹#›
Clustering Algorithms
K-means and its variants
Hierarchical clustering
Density-based clustering
02/14/2018 Introduction to Data Mining, 2nd Edition
‹#›
K-means Clustering
Partitional clustering approach
Number of clusters, K, must be specified
Each cluster is associated with a centroid (center point)
Each point is assigned to the cluster with the closest centroid
The basic algorithm is very simple
13. 02/14/2018 Introduction to Data Mining, 2nd Edition
‹#›
Example of K-means Clustering
02/14/2018 Introduction to Data Mining, 2nd Edition
‹#›
Example of K-means Clustering
02/14/2018 Introduction to Data Mining, 2nd Edition
‹#›
K-means Clustering – Details
Initial centroids are often chosen randomly.
14. Clusters produced vary from one run to another.
The centroid is (typically) the mean of the points in the cluster.
‘Closeness’ is measured by Euclidean distance, cosine
similarity, correlation, etc.
K-means will converge for common similarity measures
mentioned above.
Most of the convergence happens in the first few iterations.
Often the stopping condition is changed to ‘Until relatively few
points change clusters’
Complexity is O( n * K * I * d )
n = number of points, K = number of clusters,
I = number of iterations, d = number of attributes
02/14/2018 Introduction to Data Mining, 2nd Edition
‹#›
Evaluating K-means Clusters
Most common measure is Sum of Squared Error (SSE)
For each point, the error is the distance to the nearest cluster
To get SSE, we square these errors and sum them.
x is a data point in cluster Ci and mi is the representative point
for cluster Ci
can show that mi corresponds to the center (mean) of the
cluster
Given two sets of clusters, we prefer the one with the smallest
error
One easy way to reduce SSE is to increase K, the number of
clusters
A good clustering with smaller K can have a lower SSE than a
poor clustering with higher K
15. 02/14/2018 Introduction to Data Mining, 2nd Edition
‹#›
Two different K-means Clusterings
Sub-optimal Clustering
Optimal Clustering
Original Points
02/14/2018 Introduction to Data Mining, 2nd Edition
‹#›
Limitations of K-means
K-means has problems when clusters are of differing
Sizes
Densities
Non-globular shapes
K-means has problems when the data contains outliers.
02/14/2018 Introduction to Data Mining, 2nd Edition
‹#›
Limitations of K-means: Differing Sizes
16. Original Points
K-means (3 Clusters)
02/14/2018 Introduction to Data Mining, 2nd Edition
‹#›
Limitations of K-means: Differing Density
Original Points
K-means (3 Clusters)
02/14/2018 Introduction to Data Mining, 2nd Edition
‹#›
Limitations of K-means: Non-globular Shapes
Original Points
K-means (2 Clusters)
17. 02/14/2018 Introduction to Data Mining, 2nd Edition
‹#›
Overcoming K-means Limitations
Original PointsK-means Clusters
One solution is to use many clusters.
Find parts of clusters, but need to put together.
02/14/2018 Introduction to Data Mining, 2nd Edition
‹#›
Overcoming K-means Limitations
Original PointsK-means Clusters
02/14/2018 Introduction to Data Mining, 2nd Edition
‹#›
Overcoming K-means Limitations
18. Original PointsK-means Clusters
02/14/2018 Introduction to Data Mining, 2nd Edition
‹#›
Importance of Choosing Initial Centroids
02/14/2018 Introduction to Data Mining, 2nd Edition
‹#›
Importance of Choosing Initial Centroids
02/14/2018 Introduction to Data Mining, 2nd Edition
19. ‹#›
Importance of Choosing Initial Centroids …
02/14/2018 Introduction to Data Mining, 2nd Edition
‹#›
Importance of Choosing Initial Centroids …
02/14/2018 Introduction to Data Mining, 2nd Edition
‹#›
Problems with Selecting Initial Points
If there are K ‘real’ clusters then the chance of selecting one
centroid from each cluster is small.
Chance is relatively small when K is large
If clusters are the same size, n, then
For example, if K = 10, then probability = 10!/1010 = 0.00036
Sometimes the initial centroids will readjust themselves in
20. ‘right’ way, and sometimes they don’t
Consider an example of five pairs of clusters
02/14/2018 Introduction to Data Mining, 2nd Edition
‹#›
10 Clusters Example
Starting with two initial centroids in one cluster of each pair of
clusters
02/14/2018 Introduction to Data Mining, 2nd Edition
‹#›
10 Clusters Example
Starting with two initial centroids in one cluster of each pair of
clusters
02/14/2018 Introduction to Data Mining, 2nd Edition
‹#›
21. Solution
s to Initial Centroids Problem
Multiple runs
Helps, but probability is not on your side
Sample and use hierarchical clustering to determine initial
centroids
Select more than k initial centroids and then select among these
initial centroids
Select most widely separated
Generate a larger number of clusters and then perform a
hierarchical clustering
02/14/2018 Introduction to Data Mining, 2nd Edition
‹#›
Hierarchical Clustering
Produces a set of nested clusters organized as a hierarchical tree
Can be visualized as a dendrogram
A tree like diagram that records the sequences of merges or
splits
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Strengths of Hierarchical Clustering
Do not have to assume any particular number of clusters
Any desired number of clusters can be obtained by ‘cutting’ the
dendrogram at the proper level
They may correspond to meaningful taxonomies
Example in biological sciences (e.g., animal kingdom)
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Hierarchical Clustering
Two main types of hierarchical clustering
Agglomerative:
23. Start with the points as individual clusters
At each step, merge the closest pair of clusters until only one
cluster (or k clusters) left
Divisive:
Start with one, all-inclusive cluster
At each step, split a cluster until each cluster contains an
individual point (or there are k clusters)
Traditional hierarchical algorithms use a similarity or distance
matrix
Merge or split one cluster at a time
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Agglomerative Clustering Algorithm
Most popular hierarchical clustering technique
Basic algorithm is straightforward
Compute the proximity matrix
Let each data point be a cluster
24. Repeat
Merge the two closest clusters
Update the proximity matrix
Until only a single cluster remains
Key operation is the computation of the proximity of two
clusters
Different approaches to defining the distance between clusters
distinguish the different algorithms
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‹#›
Proximity Matrix
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‹#›
Starting Situation
28. C4
C5
Proximity Matrix
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Intermediate Situation
We want to merge the two closest clusters (C2 and C5) and
update the proximity matrix.
36. Proximity Matrix
MIN
MAX
Group Average
Distance Between Centroids
Other methods driven by an objective function
Ward’s Method uses squared error
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How to Define Inter-Cluster Similarity
38. Proximity Matrix
MIN
MAX
Group Average
Distance Between Centroids
Other methods driven by an objective function
Ward’s Method uses squared error
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How to Define Inter-Cluster Similarity
41. Proximity Matrix
MIN
MAX
Group Average
Distance Between Centroids
Other methods driven by an objective function
Ward’s Method uses squared error
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How to Define Inter-Cluster Similarity
43. Proximity Matrix
MIN
MAX
Group Average
Distance Between Centroids
Other methods driven by an objective function
Ward’s Method uses squared error
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MIN or Single Link
Proximity of two clusters is based on the two closest points in
the different clusters
Determined by one pair of points, i.e., by one link in the
proximity graph
Example:
45. 2
3
4
5
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Strength of MIN
Original Points
Six Clusters
Can handle non-elliptical shapes
02/14/2018 Introduction to Data Mining, 2nd Edition
46. ‹#›
Limitations of MIN
Original Points
Two Clusters
Sensitive to noise and outliers
Three Clusters
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MAX or Complete Linkage
Proximity of two clusters is based on the two most distant
points in the different clusters
Determined by all pairs of points in the two clusters
Distance Matrix:
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Hierarchical Clustering: MAX
Nested Clusters
Dendrogram
1
2
3
4
5
6
1
2
48. 5
3
4
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Strength of MAX
Original Points
Two Clusters
Less susceptible to noise and outliers
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Limitations of MAX
49. Original Points
Two Clusters
Tends to break large clusters
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Group Average
Proximity of two clusters is the average of pairwise proximity
between points in the two clusters.
Need to use average connectivity for scalability since total
proximity favors large clusters
Distance Matrix:
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Hierarchical Clustering: Group Average
Nested Clusters
Dendrogram
1
2
3
4
5
6
1
51. 2
5
3
4
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Hierarchical Clustering: Group Average
Compromise between Single and Complete Link
Strengths
Less susceptible to noise and outliers
Limitations
Biased towards globular clusters
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52. ‹#›
Cluster Similarity: Ward’s Method
Similarity of two clusters is based on the increase in squared
error when two clusters are merged
Similar to group average if distance between points is distance
squared
Less susceptible to noise and outliers
Biased towards globular clusters
Hierarchical analogue of K-means
Can be used to initialize K-means
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Hierarchical Clustering: Comparison
Group Average
Ward’s Method
56. 4
5
6
1
2
3
4
5
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Hierarchical Clustering: Time and Space requirements
O(N2) space since it uses the proximity matrix.
N is the number of points.
O(N3) time in many cases
There are N steps and at each step the size, N2, proximity
57. matrix must be updated and searched
Complexity can be reduced to O(N2 log(N) ) time with some
cleverness
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Hierarchical Clustering: Problems and Limitations
Once a decision is made to combine two clusters, it cannot be
undone
No global objective function is directly minimized
Different schemes have problems with one or more of the
following:
Sensitivity to noise and outliers
Difficulty handling clusters of different sizes and non-globular
shapes
Breaking large clusters
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Cluster Validity
For supervised classification we have a variety of measures to
evaluate how good our model is
Accuracy, precision, recall
For cluster analysis, the analogous question is how to evaluate
the “goodness” of the resulting clusters?
But “clusters are in the eye of the beholder”!
Then why do we want to evaluate them?
To avoid finding patterns in noise
To compare clustering algorithms
To compare two sets of clusters
To compare two clusters
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‹#›
59. Clusters found in Random Data
Random Points
K-means
Complete Link
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‹#›
Determining the clustering tendency of a set of data, i.e.,
distinguishing whether non-random structure actually exists in
the data.
Comparing the results of a cluster analysis to externally known
results, e.g., to externally given class labels.
Evaluating how well the results of a cluster analysis fit the data
without reference to external information.
- Use only the data
Comparing the results of two different sets of cluster analyses
to determine which is better.
Determining the ‘correct’ number of clusters.
60. For 2, 3, and 4, we can further distinguish whether we want to
evaluate the entire clustering or just individual clusters.
Different Aspects of Cluster Validation
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Numerical measures that are applied to judge various aspects of
cluster validity, are classified into the following three types.
External Index: Used to measure the extent to which cluster
labels match externally supplied class labels.
Entropy
Internal Index: Used to measure the goodness of a clustering
structure without respect to external information.
Sum of Squared Error (SSE)
Relative Index: Used to compare two different clusterings or
clusters.
Often an external or internal index is used for this function,
e.g., SSE or entropy
Sometimes these are referred to as criteria instead of indices
However, sometimes criterion is the general strategy and index
61. is the numerical measure that implements the criterion.
Measures of Cluster Validity
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‹#›
Two matrices
Proximity Matrix
Ideal Similarity Matrix
One row and one column for each data point
An entry is 1 if the associated pair of points belong to the same
cluster
An entry is 0 if the associated pair of points belongs to different
clusters
Compute the correlation between the two matrices
Since the matrices are symmetric, only the correlation between
n(n-1) / 2 entries needs to be calculated.
High correlation indicates that points that belong to the same
cluster are close to each other.
Not a good measure for some density or contiguity based
clusters.
Measuring Cluster Validity Via Correlation
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Measuring Cluster Validity Via Correlation
Correlation of ideal similarity and proximity matrices for the K-
means clusterings of the following two data sets.
Corr = -0.9235
Corr = -0.5810
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‹#›
Order the similarity matrix with respect to cluster labels and
inspect visually.
Using Similarity Matrix for Cluster Validation
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Using Similarity Matrix for Cluster Validation
Clusters in random data are not so crisp
K-means
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‹#›
Using Similarity Matrix for Cluster Validation
Clusters in random data are not so crisp
Complete Link
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Clusters in more complicated figures aren’t well separated
Internal Index: Used to measure the goodness of a clustering
structure without respect to external information
SSE
SSE is good for comparing two clusterings or two clusters
(average SSE).
Can also be used to estimate the number of clusters
Internal Measures: SSE
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Internal Measures: SSE
SSE curve for a more complicated data set
65. SSE of clusters found using K-means
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Correlation of ideal similarity and proximity matrices for the K-
means clusterings of the following two data sets.
Statistical Framework for Correlation
Corr = -0.9235
Corr = -0.5810
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Cluster Cohesion: Measures how closely related are objects in a
66. cluster
Example: SSE
Cluster Separation: Measure how distinct or well-separated a
cluster is from other clusters
Example: Squared Error
Cohesion is measured by the within cluster sum of squares
(SSE)
Separation is measured by the between cluster sum of squares
Where |Ci| is the size of cluster i
Internal Measures: Cohesion and Separation
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68. K=2 clusters:
K=1 cluster:
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A proximity graph based approach can also be used for cohesion
and separation.
Cluster cohesion is the sum of the weight of all links within a
cluster.
Cluster separation is the sum of the weights between nodes in
the cluster and nodes outside the cluster.
Internal Measures: Cohesion and Separation
69.
70. cohesion
separation
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“The validation of clustering structures is the most difficult
and frustrating part of cluster analysis.
Without a strong effort in this direction, cluster analysis will
remain a black art accessible only to those true believers who
have experience and great courage.”
Algorithms for Clustering Data, Jain and Dubes
Final Comment on Cluster Validity
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Discovered Clusters Industry Group
1
Applied-Matl-DOWN,Bay-Network-Down,3-COM-DOWN,
Cabletron-Sys-DOWN,CISCO-DOWN,HP-DOWN,
DSC-Comm-DOWN,INTEL-DOWN,LSI-Logic-DOWN,
Micron-Tech-DOWN,Texas-Inst-Down,Tellabs-Inc-Down,
Natl-Semiconduct-DOWN,Oracl-DOWN,SGI-DOWN,
Sun-DOWN
Technology1-DOWN
2
Apple-Comp-DOWN,Autodesk-DOWN,DEC-DOWN,
ADV-Micro-Device-DOWN,Andrew-Corp-DOWN,
Computer-Assoc-DOWN,Circuit-City-DOWN,
Compaq-DOWN, EMC-Corp-DOWN, Gen-Inst-DOWN,
Motorola-DOWN,Microsoft-DOWN,Scientific-Atl-DOWN
Technology2-DOWN
3
Fannie-Mae-DOWN,Fed-Home-Loan-DOWN,
107. -
=
=
Total
BSS
WSS
SSE
JOURNAL OF APPLIED BEHAVIOR ANALYSIS
WHAT MAKES EXTINCTION WORK: AN ANALYSIS OF
PROCEDURAL FORM AND FUNCTION
BRIAN A. IWATA
THE UNIVERSITY OF FLORIDA
GARY M. PACE
THE KENNEDY INSTITUTE, BALTIMORE, MARYLAND
GLYNNIS EDWARDS COWDERY
WE CARE, INC., BERKELEY, CALIFORNIA
108. AND
RAYMOND G. MILTENBERGER
NORTH DAKOTA STATE UNIVERSITY
We examined methods for determining how extinction should be
applied to different functions of
self-injurious behavior (SIB). Assessment data indicated that
the head banging of 3 children with
developmental disabilities was maintained by different
reinforcement contingencies: One subject's
SIB was positively reinforced by attention from adults, the 2nd
subject's SIB was negatively reinforced
by escape from educational tasks, and the 3rd subject's SIB
appeared to be automatically reinforced
or "self-stimulatory" in nature. Three functional variations of
extinction-EXT (attention), EXT
(escape), and EXT (sensory)-were evaluated, and each subject
was exposed to at least two of these
variations in reversal or multiple baseline designs. Reductions
in SIB were observed only when
implementation of "extinction" involved the discontinuation of
reinforcement previously shown to
be responsible for maintaining the behavior. These results
highlight important differences among
109. treatment techniques based on the same behavioral principle
(extinction) when applied to topo-
graphically similar but functionally dissimilar responses, and
further illustrate the practical impli-
cations of a functional analysis of behavior disorders for
designing, selecting, and classifying ther-
apeutic interventions.
DESCRIPTORS: extinction, functional analysis, self-injurious
behavior
Research on the functional analysis of severe
behavior disorders has produced a variety of inter-
ventions based on the modification of antecedent
events that occasion behavior problems as well as
the consequences that maintain them (see Iwata,
Vollmer, & Zarcone, 1990, and Mace, Lalli, &
Lalli, 1991, for recent reviews). Much of the em-
phasis in treatment has been on strengthening new
stimulus-response-consequence relationships. By
contrast, relatively little attention has been paid to
eliminating reinforcement that maintained the be-
This research was supported in part by a grant from the
Developmental Disabilities Planning Council and the Florida
Department of Health and Rehabilitative Services.
110. Reprints may be obtained from Brian Iwata, Psychology
Department, University of Florida, Gainesville, Florida 3261 1.
havior problem in the first place, even though many
of the interventions described in the literature im-
plicitly contained such a provision. That is, pun-
ishment of Response A is almost always combined
with the cessation of reinforcement; likewise, treat-
ment involving reinforcement of Response B as a
replacement for Response A usually coincides with
the termination of reinforcement for Response A.
Moreover, data from several recent studies suggest
that the effects of reinforcement-based interventions
may be limited unless extinction (withholding the
behavior's maintaining reinforcers) is included as
part of the treatment program. It has been shown,
for example, that interventions based on the de-
velopment of communicative responses (Carr &
Durand, 1985) and on behavioral momentum
(Mace & Belfiore, 1990) produced either mixed
131
1994127,131-144 NUMBER I (SPRING 1994)
111. BRIAN A. IWATA et al.
results (Wacker et al., 1990) or no treatment effect
(Zarcone, Iwata, Hughes, & Vollmer, 1993) when
implemented without extinction, and that the crit-
ical feature of procedures such as differential rein-
forcement of other behavior (DRO) contingencies
appears to be the extinction component rather than
the reinforcement component (Mazaleski, Iwata,
Vollmer, Zarcone, & Smith, 1993).
The assessment and treatment of self-injurious
behavior (SIB) provide an important context for
the examination of extinction, because it has been
demonstrated that SIB can be maintained through
a variety of operant mechanisms. Nevertheless, be-
cause the "discontinuation of reinforcement" for
behavior problems in general often involves ces-
sation of ongoing events, this procedure has become
so common that some textbooks define extinction
solely through reference to "ignoring," time-out,
and other examples of stimulus termination (e.g.,
112. LaVigna & Donnellan, 1986). However, research
has shown that procedural time-out can serve dif-
ferent functions, not all of which are behavior re-
ducing (Plummer, Baer, & LeBlanc, 1977; Solnick,
Rincover, & Peterson, 1977), and the same is true
of procedural approaches to defining extinction.
Ignoring misbehavior may represent extinction in
some cases but not in others; conversely, the correct
application of extinction may require termination
of events in some cases but continuation in others.
The procedures that define extinction in a given
situation are determined by the specific nature of
the reinforcement to be "discontinued."
In cases in which SIB was maintained by social-
positive reinforcement in the form of adult atten-
tion, extinction consisted of withholding attention
or terminating it contingent on the occurrence of
SIB (e.g., Day, Rea, Schussler, Larsen, & Johnson,
1988; Lovaas & Simmons, 1969). By contrast, SIB
maintained through social-negative reinforcement
in the form of escape from task demands has been
extinguished by preventing escape; in other words,
continuing and not terminating the ongoing sit-
uation (e.g., Iwata, Pace, Kalsher, Cowdery, &
113. Cataldo, 1990; Repp, Felce, & Barton, 1988).
Finally, SIB apparently maintained by nonsocial,
automatic reinforcement (e.g., sensory stimulation)
has shown extinction-like decreases when the in-
dividuals wore equipment that allowed the behav-
ior to occur, but attenuated its consequences (e.g.,
Rincover & Devany, 1982). Thus, at least three
functional variations of extinction have been used
as treatment for SIB, each designed to terminate a
different source of reinforcement, and each ame-
nable to a number of procedural modifications and
descriptive labels.
Although extinction procedures are clearly unique
from the standpoint of both form (specific therapist
actions) and function (the maintaining contingen-
cies to which they apply), these variations are not
well differentiated through existing terminology.
Planned ignoring, the label perhaps most often
applied to extinction of attention-maintained be-
havior (Nelson & Rutherford, 1983), provides an
adequate description of the therapist's response, but
it does not describe the underlying behavioral pro-
cess (extinction), nor does it identify the source of
114. reinforcement being withheld (attention). Escape
extinction, a term used to describe extinction of
escape-maintained behavior (Iwata, Pace, Kalsher,
Cowdery, & Cataldo, 1990), specifies the relevant
process as well as the reinforcer, but not the pro-
cedure. Finally, sensory extinction, which refers to
a variety of techniques designed to attenuate stim-
ulation directly produced by a response (Rincover,
1978; Rincover, Cook, Peoples, & Packard, 1979),
has the same descriptive characteristics as escape
extinction (it specifies process and reinforcer, but
not procedure); in addition, the wording is awk-
ward because nothing "sensory" is extinguished.
In an attempt to promote brevity as well as con-
sistency of terminology, we have adopted through-
out this paper the convention of referring to dif-
ferentfunctional variations of extinction by using
the abbreviation "EXT" followed in parentheses
by the source of reinforcement withheld, as in EXT
(attention), EXT (escape), and EXT (sensory). We
chose "EXT" (attention) over "attention EXT"
because the former places emphasis on behavioral
process, with the reinforcer incidental, whereas the
latter connotes that attention is extinguished.
115. This terminology is still incomplete because it
does not differentiate procedural variations within
132
VARIATIONS OF EXTINCTION
a given functional class of extinction techniques.
For example, EXT (attention) may take different
forms depending on the situational context in which
it is applied. If the target behavior occurs in the
absence of ongoing social interaction, EXT (atten-
tion) requires no response from the therapist and
simply consists of withholding attention that pre-
viously followed the behavior. A more complicated
situation exists if the target behavior occurs while
the therapist is interacting with the client. In this
case, withholding reinforcement [EXT (attention)]
would consist of terminating the interaction.' Be-
cause similar variations are also characteristic of
both EXT (escape) and EXT (sensory), we did not
attempt to specify any particular procedure by way
of descriptive label; this practice is consistent with
116. terms such as DRO, time-out, punishment, and so
forth, all of which require further elaboration.
A reasonable conclusion based on descriptions
of behavior, procedure, and outcome reported in
the above studies is that extinction designed for
SIB serving one function may have little or no
therapeutic effect on SIB serving a different func-
tion. Given the variations of extinction described
previously and the maintaining contingencies for
which they might be used, it is possible to construct
a contingency matrix such as that found in Figure
1, which allows predictions about behavioral out-
come. For example, elimination of social reinforce-
ment for SIB using EXT (attention) or EXT (es-
cape) will not interfere with the delivery of sensory
(automatic) reinforcement, and EXT (sensory)
would have no effect on social sources of reinforce-
ment. Most seriously, EXT (attention) applied to
escape-maintained SIB (i.e., stimulus removal con-
tingent on escape behavior) and, conversely, EXT
(escape) applied to attention-maintained SIB (i.e.,
stimulus continuation contingent on attention-get-
ting behavior) may be countertherapeutic and se-
riously exacerbate the behavior problem. At the
117. In this example, it is unclear if the subsequent change
in behavior reflects withholding of contingent reinforcement
that maintained SIB (extinction) or removal of ongoing re-
inforcement (time-out). In either case, and from a practical
standpoint, the only means of not reinforcing the behavior
consists of terminating interaction.
FUNCTIONAL VARIATIONS OF EXTINCTION
0
LL
0
z
LU
0
z
1
z
0
0
z
Ir.2 f ifis_---_..Treatment
118. Figure 1. Expected outcomes when functional variations
of extinction are applied to different maintaining contingen-
cies for SIB.
present time, evidence directly supporting these pre-
dictions can be found in only a few studies. Research
on the treatment of self-injurious escape behavior,
for example, sometimes has included a baseline
condition in which time-out from educational tasks
was made contingent on SIB (Iwata, Pace, Kalsher,
Cowdery, & Cataldo, 1990; Repp et al., 1988;
Steege et al., 1990). In effect, this condition pro-
cedurally amounted to EXT (attention) but was
associated with increases in escape-maintained SIB.
In the present study, we provide an empirical
evaluation of the key predictions found in Figure
1 by conducting a comparative analysis of extinc-
tion techniques. The relative effects of three func-
tional variations of extinction were examined when
applied to the same topography of SIB maintained
by three different contingencies of reinforcement.
METHOD
119. Subjects and Setting
Subjects were selected for participation based on
(a) their having similar topographies of SIB, and
(b) the outcomes of functional analysis baselines
indicating that their SIB was maintained by dif-
ferent sources of reinforcement. Three children with
developmental disabilities who met these criteria
were included as participants. All of them exhibited
head banging that produced contusions or lacera-
tions on the head and face. Donnie, a 7-year-old
boy with severe mental retardation, was ambulatory
133
BRIAN A. IWATA et al.
and could feed himself. He did not follow vocal
instructions, although he had a fairly good imitative
repertoire, and he communicated his needs by
pointing. Donnie's parents could not identify any
situations that were predictive of either high or low
120. levels of SIB. His previous treatments consisted of
response interruption, redirection to another activ-
ity, time-out, and differential reinforcement. Jack,
a 12-year-old boy with severe mental retardation,
was nonambulatory but could move his wheelchair
over short distances, feed himself, and manipulate
small objects. He followed a few instructions and
communicated primarily through idiosyncratic ges-
ture (i.e., reaching and making a high-pitched vocal
noise). Jack's parents and teachers reported that his
SIB seemed to occur as part of a tantrum, although
they could not reliably describe the types of situ-
ations in which tantrums occurred. His previous
treatments consisted of time-out and differential
reinforcement. Millie, an 8-year-old girl with mod-
erate mental retardation, was ambulatory, could
feed herself, and occasionally followed simple in-
structions. Although she did not exhibit any ex-
pressive language, she appeared to be socially re-
sponsive to adults (e.g., she approached adults when
they were nearby, smiled at them, etc.). Millie's
parents indicated that her SIB occurred "most of
the time," but became worse when she did not
"get her way." Her previous treatments consisted
of verbal reprimands, response interruption, man-
121. ual restraint, redirection, and differential reinforce-
ment. She was also placed in a hard seizure helmet
as a means of protection when her SIB was deemed
to be "uncontrollable."
Sessions were usually conducted individually in
therapy rooms containing one-way observation win-
dows, but occasionally (due to scheduling neces-
sities) were run in a large group area where two or
three other clients and one or two other staff mem-
bers were present but located in a different part of
the room (i.e., at least 6 m away). This periodic
change in location seemed to have no effect on the
subjects' behavior. Sessions were 15 min in duration
and usually were conducted 5 days per week, with
four to eight sessions daily and at least 15-min
breaks between sessions.
Response Measurement and Reliability
SIB was defined as any audible contact between
the head or face and either a fist or an object (e.g.,
furniture or walls). Data were recorded using one
of two methods: (a) on paper during continuous
10-s intervals, which were cued by cassette tape;
122. or (b) on a hand-held computer (Panasonic Model
RL-H1800). All data were converted into per-
centage of 10-s intervals during which one or more
instances of SIB occurred. Data were also collected
on a variety of experimenter behaviors (delivery of
instructions or attention, withdrawal of instructions
or attention, placement and removal of apparatus)
as a means of monitoring procedural consistency;
these data indicated that experimenter compliance
exceeded 90% across all categories.
Interobserver agreement was assessed by having
a second observer simultaneously but independently
record data during 23% of all sessions. Agreement
percentages were calculated based on interval-by-
interval comparison of observers' records by divid-
ing the number of agreements by the number of
agreements plus disagreements and multiplying by
100%. Mean agreement was 92% across subjects,
with all values exceeding 86%.
Experimental Designs and Sequence
During the initial baseline, subjects were exposed
to a series of assessment conditions in a multiele-
123. ment design (Sidman, 1960; Ulman & Sulzer-Aza-
roff, 1975) to identify the maintaining variables
for their SIB. Subsequently, each subject was ex-
posed to two or more functional variations of ex-
tinction by way of reversal or multiple baseline
designs. Because the specific conditions and their
order of presentation were determined by subjects'
baseline performances, more complete details are
provided in the Results section for each subject.
Functional Analysis Baseline
Subjects were exposed to four conditions based
on Iwata, Dorsey, Slifer, Bauman, and Richman
(1982). A brief description of each condition is
provided here.
Attention. This condition was designed to test
134
VARIATIONS OF EXTINCTION
124. for positive reinforcement (attention) as a main-
taining variable for SIB. An experimenter initially
placed the subject in contact with toys that were
in the room, then proceeded to ignore the subject
while seeming to do paperwork. Contingent on the
occurrence of SIB, the experimenter expressed con-
cern (e.g., "Stop. Don't do that; you'll hurt your-
self.") and briefly interrupted the response.
Demand. This condition was a test for negative
reinforcement (escape from demands) as a main-
taining variable. An experimenter presented aca-
demic tasks (e.g., object identification, sorting,
drawing, and other tasks requiring simple motor
responses) comparable to those found in the sub-
ject's individual educational plan. Tasks were pre-
sented in a discrete-trial format approximately once
every 30 s. The experimenter used modeling and
physical guidance as supplementary prompts to
produce compliance, delivered praise contingent on
correct responses, and implemented a 30-s time-
out contingent on the occurrence of SIB. The time-
out consisted of removing the materials from the
table and turning away from the subject.
125. Alone. By restricting access to social and material
sources of stimulation, this condition provided a
test for SIB maintained by nonsocial (automatic)
reinforcement. The subject was observed while alone
in the room (which was empty except for a chair
or couch).
Play. This condition served as a control. The
experimenter provided continuous access to toys,
delivered praise approximately every 30 s contin-
gent on the absence of SIB, and ignored occurrences
of SIB.
Extinction Conditions
Three variations of extinction were evaluated,
each designed to discontinue a different source of
reinforcement for SIB. An attempt was made to
implement each type of extinction with each sub-
ject, but this was not always possible if (a) little or
no SIB occurred in a given baseline condition, or
(b) the baseline condition itself was not amenable
to implementation of the procedure as described.
For example, it was not possible to prevent escape
from tasks (i.e., to withhold negative reinforce-
126. ment) during the alone baseline, because no tasks
were presented initially.
EXT (attention). This variation of extinction
was designed to discontinue positive reinforcement
in the form of attention delivered by the experi-
menter. EXT (attention) already was a component
of three of the baseline conditions: during the de-
mand condition, attention was withdrawn contin-
gent on SIB; during the alone condition, no adult
was present to deliver any attention; and during
the play condition, attention was withheld contin-
gent on SIB. Thus, the attention condition was the
only baseline on which EXT (attention) could be
introduced as a new manipulation. This extinction
contingency consisted of having the experimenter
ignore (not attend to) SIB, and was combined with
experimenter attention for the absence of SIB, which
was delivered on a 30-s DRO schedule. Occur-
rences of SIB reset the DRO interval.
EXT (escape). This variation of extinction dis-
continued negative reinforcement in the form of
escape from tasks. It was implemented during the
127. demand condition, which was the only condition
containing a task requirement. During EXT (es-
cape), learning trials continued as during baseline
but were not terminated contingent on SIB. Instead,
the experimenter physically guided the subject to
comply with the instruction and continued the ses-
sion according to schedule. It has been noted pre-
viously (Iwata, Pace, Kalsher, Cowdery, & Cataldo,
1990) that the physical guidance component of
this intervention may represent a punishment con-
tingency. However, (a) guidance was the inevitable
consequence of noncompliance even during base-
line, and (b) behavior change observed following
implementation of this procedure in the above study
as well as in others (e.g., Goh & Iwata, 1994;
Repp et al., 1988) showed either temporary burst-
ing or gradual decreases consistent with extinction
processes.
EXT (sensory). This variation of extinction was
designed to attenuate the sensory consequences pro-
duced by subjects' head banging, and could be
implemented across any of the baseline conditions.
Each subject was fitted with an oversized helmet
(either a seizure or a lacrosse helmet), which was
128. 135
BRIAN A. IWATA et al.
reinforced with additional padding. During EXT
(sensory), the helmet was placed on the subject's
head at the beginning of a session and remained
in place throughout (subjects never attempted to
remove the helmets). An extension of this "non-
contingent" helmet condition was implemented for
Donnie and is described below.
RESULTS
Donnie
Figure 2 shows the results obtained for Donnie.
He exhibited a considerable amount of SIB across
all of the baseline conditions, thus permitting a
series of manipulations on each baseline. Moderate
levels of SIB were observed during the demand,
attention, and play conditions (lower three panels),
129. whereas SIB occurred almost continuously during
the alone condition (upper panel) containing no
access to social stimulation, play materials, or tasks.
These data suggested that Donnie's SIB was main-
tained by factors independent of the social and
physical environment and were consistent with be-
havior reinforced by directly produced, automatic
consequences.
On the alone baseline (top panel), EXT (sensory)
was implemented in a reversal (ABAB) design, and
results showed decreases in SIB associated with the
helmet intervention. The final condition on the
alone baseline involved two modifications of the
EXT (sensory) procedure. First, play materials that
Donnie was observed to manipulate during the
original play baseline were introduced. Second, the
protective helmet was applied only contingent on
the occurrence of SIB. As long as SIB did not occur,
Donnie was free to play with the toys and move
about without wearing the helmet. When SIB oc-
curred, an experimenter, who was in the room but
did not interact with Donnie during the session,
placed the helmet on Donnie for a 2-min time-
out, during which the toys were removed from
130. sight. These procedural modifications were based
on results reported by Dorsey, Iwata, Reid, and
Davis (1982), who found that it was possible to
transfer control of SIB from a noncontingent to a
contingent helmet condition. SIB increased initially
when this change was made on the alone baseline,
but eventually decreased to a level similar to that
observed during the EXT (sensory) conditions.
On the demand baseline (second panel from the
top), the introduction of EXT (sensory) was asso-
ciated with a rapid and large decrease in Donnie's
SIB. This reduction occurred in spite of the fact
that the original baseline contingency for SIB-
EXT (attention) or, alternatively, escape from the
task contingent on SIB-remained in effect. Next,
EXT (sensory) was removed and EXT (escape) was
implemented; this resulted in an increase in SIB to
its baseline level. Finally, the contingent helmet
procedure was combined with EXT (escape). The
experimenter presented learning trials as before and,
contingent on SIB, guided Donnie through the task
and then placed the helmet on him. The helmet
remained on for approximately 2 min (four learning
131. trials). This condition was associated with a decrease
in SIB similar to that seen during the previous EXT
(sensory) condition.
On the attention baseline (third panel from the
top), the introduction of EXT (attention) had no
effect on Donnie's SIB. During the next condition,
EXT (sensory), SIB decreased even though it pro-
duced attention from the experimenter. The final
procedure implemented on this baseline consisted
of EXT (attention) combined with a 2-min time-
out in the helmet contingent on occurrences of SIB,
and was associated with a reduction in SIB similar
to that seen in the EXT (sensory) condition.
On the play baseline (bottom panel), which con-
tained an EXT (attention) component, no decrease
in SIB was observed until EXT (sensory) was in-
troduced. Subsequently, SIB increased temporarily
but decreased again when the procedure was changed
to a 2-min time-out in the helmet contingent on
SIB.
Jack
The initial baseline of Figure 3 shows the results
132. of Jack's assessment. He exhibited little or no SIB
except during the demand condition, which con-
tained two distinctive features: the presentation of
task demands and a brief time-out from the task
contingent on SIB. The time-out component pro-
136
DONNIE
100- Baseline
800
n:n -a
40 -
20 -
VARIATIONS OF EXTINCTION
133. r EXT(sensory) 1
BL I Toys + Conting(
-a- Ati
-a-- -D
-.*-- Al4
-a- Pli
ent Helmet
ttention
emand
lone
lay
1 ---- -i-
40 EXT Contingent Helmet
Baseline EXT(sensory) (escape) + EXT(escape)
20
o r , . .
40 Contingent Helmet
134. Baseline EXT(attn) EXT(sensory) + EXT(attn)
20
40 Contingent
Baseline EXT(sensory) Helmet
20
0 20 40 60 80 100
137
co)
-J
cn
w
H
z
uL
135. 0
Lu
w
z
w
0L
20 40 60 80 1 00
SESSIONS
Figure 2. Percentage of intervals of SIB exhibited by Donnie
across experimental conditions.
ou -1
A
II
136. BRIAN A. IWATA et al.
EXT(sensory)
100
co
C,)
-J
Er
w
z
LL
0
LLJ
z
LU
cc
137. LLJw-
80
60
40
20
0
-H0.
SESSIONS
Figure 3. Percentage of intervals of SIB exhibited by Jack
across experimental conditions.
cedurally resembled EXT (attention) but appeared
to function as (negative) reinforcement for escape
behavior. Because little or no SIB was observed
during other conditions, all subsequent manipu-
lations were made on the demand baseline. EXT
(sensory) and EXT (escape) were implemented con-
138. currently and resulted in a large decrease in Jack's
SIB. A partial reversal was then conducted in which
EXT (escape) was removed while EXT (sensory)
remained in effect; this change resulted in an in-
crease in Jack's SIB to its original baseline level.
SIB decreased again when EXT (escape) was re-
introduced, and it remained low following the re-
moval of EXT (sensory).
Millie
Figure 4 shows the results obtained for Millie.
During the initial baseline assessment, her SIB oc-
curred almost exclusively during the attention con-
dition, suggesting that the behavior was maintained
by social-positive reinforcement. Very little SIB was
observed during the play and demand conditions,
both of which contained a brief time-out from
attention contingent on SIB, and SIB decreased
throughout the alone condition, which contained
no attention whatsoever. Thus, Millie's assessment
data revealed not only a reinforcement effect during
the attention condition but also an apparent ex-
tinction effect during others.
139. In light of these results, subsequent interventions
were implemented only on the attention baseline.
EXT (attention) with attention delivered a 30-s
DRO schedule was introduced concurrent with EXT
(sensory) and resulted in a large decrease in Millie's
SIB. Next, while EXT (sensory) remained in effect,
a reversal was conducted in which EXT (attention)
+ DRO was removed; this partial return to base-
line was associated with an immediate and large
increase in SIB. When EXT (attention) + DRO
was reinstated, SIB decreased to near-zero levels.
EXT (sensory) was then removed while EXT (at-
tention) + DRO remained in effect, and no increase
was observed in SIB. During this final condition,
the length of the DRO interval was gradually in-
creased to 1, 2, and finally 5 min, and SIB remained
low across all schedule changes.
138
VARIATIONS OF EXTINCTION
140. EXT(sensory)
_,4,0MILLIE
EXT(attn) + DRO
Baseline BL
-a Attention
*- Demand
-0- Alone
0 Play
20 40 60 80
SESSIONS
Figure 4. Percentage of intervals of SIB exhibited by Millie
across experimental conditions.
Summary of Key Comparisons
Table 1 contains a summary of the results from
selected baseline and extinction conditions for Don-
nie, Jack, and Millie. The data reflect reductions
or increases in SIB expressed as mean percentages
of baseline responding (EXT mean/baseline mean)
for relevant and irrelevant extinction conditions
141. compared to their appropriate baselines. Because
SIB during relevant extinction conditions usually
showed decreasing trends, comparisons based on
overall condition means would not accurately depict
end-of-treatment responding. Therefore, all per-
centages are based on the last five sessions of a
condition. For example, under "Relevant EXT,"
Donnie's mean percentage of SIB during the last
five sessions of EXT (sensory) occurred at 0.5% of
the mean SIB during the last five sessions of his
alone baseline, whereas under "Irrelevant EXT,"
his five-session mean percentage of SIB during EXT
(escape) occurred at 81.9% of his demand baseline
mean. These comparisons show that SIB for all
subjects was reduced to below 15% of its baseline
Table 1
Mean Change (Reduction or Increase) in SIB Expressed as a
Percentage of Baseline Responding for Relevant and
Irrelevant Extinction Conditions Compared to Their Relevant
Baselines. Percentages Are Based on the Last Five Sessions
of a Condition
142. Relevant EXT / baseline Irrelevant EXT / baseline
Subject Conditions compared % of BL Conditions compared %
of BL
Donnie EXT (sensory) / alone BL 0.5 EXT (escape) / demand
BL 81.9
EXT (sensory) / demand BL 6.9 EXT (attn) / attn BLa 81.7
EXT (sensory) / attn BLa 14.3
EXT (sensory) / play BL 8.2
Jack EXT (escape) / demand BL 5.4 EXT (sensory) / demand
BL 75.8
Millie EXT (attn) / attn BL 3.6 EXT (sensory) / attn BL 126.3
Mean change as % of baseline SIB 6.5 91.4
a Donnie's attention baseline consisted of only four sessions.
139
co
CO
C,)
-J
144. BRIAN A. IWATA et al.
mean during relevant extinction conditions (mean
reduction = 6.5% of baseline), but was never re-
duced to lower than 75% of baseline during irrel-
evant extinction conditions (mean reduction =
91.4% of baseline).
Follow-Up
At the completion of the study, a treatment
program designed for each subject was imple-
mented throughout the day in the appropriate sit-
uational contexts. Donnie's program consisted of
several components. First, free access to toys was
provided whenever possible (except during training
sessions, self-care routines, etc.). Second, occur-
rences of SIB were followed by wearing his padded
helmet for 2 min. Finally, and as a preventive
measure, the contingent helmet procedure was com-
bined with either EXT (attention) or EXT (escape)
depending on the situational context. If Donnie
145. exhibited SIB while participating in training, the
session was continued while he wore the helmet. If
SIB occurred at other times, the helmet was com-
bined with time-out from social interaction. Jack's
treatment consisted of EXT (escape) identical to
that described previously, and it was implemented
during all training activities. Millie's treatment con-
sisted of attention contingent on appropriate social
initiations, defined as any approach behavior while
not engaged in SIB. A 5-min DRO contingency
also was implemented with attention as the rein-
forcing consequence. If Millie exhibited SIB while
an adult was interacting with her, the adult would
turn away and ignore her until (a) Millie ap-
proached while not engaging in SIB, or (b) she
successfully completed a 5-min DRO interval. Thus,
Millie's program contained an explicit EXT (at-
tention) component.
Subjects' parents and teachers were instructed in
the use of the above procedures until they dem-
onstrated proficiency in implementation. Follow-
up contacts were faded over a 6-month period,
during which SIB occurred at well below baseline
levels for all subjects.
146. DISCUSSION
Results of this study showed that therapeutic
techniques previously defined as extinction in the
applied literature are different not only procedurally
but also in their behavioral effects when applied to
the same response topography. Each of three vari-
ations of extinction-EXT (attention), EXT (es-
cape), and EXT (sensory)-reduced SIB only when
it resulted in discontinuation of the specific source
of reinforcement maintaining the behavior. Thus,
the process of extinction is not tied to any particular
form of intervention (e.g., ignoring undesirable be-
havior); instead, it is determined by the behavior's
maintaining contingency. Moreover, the data pre-
sented here indicate that if the source of reinforce-
ment for a behavior disorder such as SIB can be
identified on a pretreatment basis, much of the
guesswork is removed from the task of selecting
an appropriate extinction technique.
Results obtained for Donnie provide the most
complete analysis in the present study because he
147. was exposed to all three functional variations of
extinction. Neither EXT (attention) nor EXT (es-
cape) was effective in reducing Donnie's SIB. His
head banging, which apparently was maintained
by sensory consequences, was reduced across all
baseline conditions when EXT (sensory) was ap-
plied, even though SIB still produced attention and
escape during the attention and demand baselines,
respectively. Jack, for whom EXT (escape) and
EXT (sensory) were evaluated explicitly as treat-
ments, was also exposed implicitly to EXT (atten-
tion). The brief time-out contingent on SIB during
his initial demand baseline closely resembled EXT
(attention), yet it actually amounted to negative
reinforcement and resulted in the highest levels of
SIB when compared to other assessment conditions.
EXT (sensory) also had little suppressive effect on
Jack's SIB, which decreased only when it no longer
produced termination of learning trials during the
EXT (escape) condition. For Millie, whose baseline
data indicated that her SIB was maintained by
positive reinforcement in the form of attention,
effective treatment consisted of EXT (attention)
combined with DRO (attending to her when she
did not exhibit SIB), whereas EXT (sensory) had
148. no apparent effect on her behavior. Millie's results
are limited in two respects. First, a stronger dem-
onstration of extinction effects would have been
provided had EXT (attention) not been combined
140
VARIATIONS OF EXTINCTION
with the DRO procedure, although recent data
(Mazaleski et al., 1993) suggest that extinction is
the major therapeutic component of DRO contin-
gencies. Second, because little or no SIB was ob-
served during her demand baseline, it was not pos-
sible to examine the effects of EXT (escape) on her
behavior.
It is important to note that the procedures used
in this study, although labeled "EXT" for each
subject, differed in two respects. First, because only
one variation of extinction was effective in reducing
SIB (a different one for each subject), the other two
variations did not functionally amount to extinc-
149. tion. We labeled all procedures similarly to reduce
confusion and to emphasize the facts that (a) each
procedure has been described as an extinction tech-
nique in the literature, and (b) procedures so labeled
might not produce reductions in behavior if they
do not terminate the behavior's maintaining con-
tingency. Based on the results obtained during as-
sessment and treatment, a more accurate description
of the procedures used with each subject might be
as follows. Donnie was exposed to EXT (sensory),
ignoring SIB or terminating interaction contingent
on SIB [labeled EXT (attention)], and task con-
tinuation and prompting contingent on SIB [la-
beled EXT (escape)). Jack was exposed to EXT
(escape), a helmet condition [labeled EXT (sen-
sory)1, and terminating interaction contingent on
SIB (his demand baseline). Millie was exposed to
EXT (attention) and a helmet condition [labeled
EXT (sensory)}. A second difference can be seen
within one of the extinction components. EXT (es-
cape) and EXT (sensory) were applied in a consis-
tent manner during treatment sessions. EXT (at-
tention), however, took two different forms: ignoring
SIB that occurred in the absence of interaction, and
150. terminating ongoing interaction contingent on the
occurrence of SIB. These differences illustrate a
point already noted: Extinction procedures can be
defined with respect to both function (the rein-
forcement contingency being discontinued) and,
within function, form (specific therapist actions).
The lack of therapeutic effects observed when a
given variation of extinction was applied to SIB
maintained by a different (irrelevant) source of re-
inforcement provides new data on some of the
limiting conditions of extinction. On the other hand,
the positive treatment effects observed during rel-
evant extinction conditions were not particularly
novel. Previous studies have reported reductions in
SIB when the reinforcer withheld during extinction
was relevant to behavioral maintenance: EXT (at-
tention) for attention-maintained SIB (e.g., Lovaas
& Simmons, 1969), EXT (escape) for escape-main-
tained SIB (e.g., Iwata, Pace, Kalsher, Cowdery,
& Cataldo, 1990), and EXT (sensory) for auto-
matically reinforced or self-stimulatory SIB (e.g.,
Rincover & Devaney, 1982). Nevertheless, these
findings have not given rise to a consistent termi-
151. nology that distinguishes one type of extinction
from another, they have not been adopted by au-
thors of most textbooks on applied behavior anal-
ysis (see Cooper, Heron, & Heward, 1987, for a
notable exception), and they have not been incor-
porated into guidelines regulating the use of be-
havioral interventions (e.g., Florida HRS Manual
160-4, 1989).
Extinction is similar to other behavioral pro-
cesses, such as reinforcement or punishment, from
which a number of therapeutic techniques can be
derived. Although this fact applies to all behavioral
interventions, the case of punishment is of greatest
concern because some of its procedural variations
are considered to be highly intrusive or otherwise
unacceptable (O'Brien & Karsh, 1990). As a result,
administrative and treatment manuals place a great
deal of emphasis on the topographical aspects of
intervention in order to promote procedural con-
sistency by specifying the acceptable limits of ther-
apist behavior when implementing a given tech-
nique. Although this approach to treatment
classification results in a well-defined system of pro-
cedures, behavioral effects may be difficult to pre-
152. dict because therapist behavior, although clearly
defined, may enter into multiple contingencies with
respect to client behavior. Thus, "planned ignor-
ing" functions as EXT (attention) for attention-
seeking behavior but as negative reinforcement for
escape behavior, whereas procedures such as "re-
direction" or other attempts to prompt compliance
with task demands function as EXT (escape) for
escape behavior but as positive reinforcement for
attention-seeking behavior. Functions other than
141
BRIAN A. IWATA et al.
EXT (sensory) that might be attributed to the hel-
met intervention used in this study are not entirely
clear at the present time, but they might include
punishment (wearing the apparatus as an aversive
event), social reinforcement (attention paired with
equipment placement), or time-out (overall re-
duced access to reinforcement while wearing the
equipment).
153. Problems may arise when any of these procedures
serves unintended functions such as those just de-
scribed. At best, these discrepancies may result in
the use of ineffective treatments described as ex-
tinction (e.g., as in ignoring automatically rein-
forced behavior); at worst, they may result in the
use of highly inappropriate treatments described
as extinction (as in ignoring or time-out for escape
behavior). In either case, failure to distinguish be-
tween the principle of extinction and the ways in
which it may be applied can lead to the erroneous
conclusion that "extinction" is a relatively ineffec-
tive intervention. When these errors are formalized
by way of regulation, an unfortunate state of affairs
may result: Procedural manuals designed to protect
persons from intrusive interventions (e.g., punish-
ment) to reduce behavior may require the use of
nonintrusive interventions (e.g., misapplied ignor-
ing or attention) that strengthen dangerous behav-
ior to the point that the intrusive intervention is
required.
Although the results of this study are limited to
consideration of extinction effects, they have im-
154. plications for the design of interventions based on
other learning mechanisms. For example, behav-
ioral function is highly relevant to the selection of
"reinforcers" delivered and withheld in differential
reinforcement contingencies (Carr & Durand, 1985),
and although social reprimands often have been
found to function as punishment, they can also
serve as positive reinforcement (Van Houten &
Doleys, 1983). Thus, data from a number of stud-
ies on the functional analysis of behavior disorders
indicate that current methods for classifying inter-
ventions are inadequate. There is a critical need to
develop classification systems and treatment man-
uals that specify not only procedures, topographies
for which they may be used, and preferred hierarchy
based on consideration of factors such as "intru-
siveness," but also how the same principle of learn-
ing may be translated into different procedures
based on differences in behavioral function (see
Iwata, Vollmer, Zarcone, & Rodgers, 1993, and
Repp & Karsh, 1990, as examples).
Because the present results indicated that iden-
tification of a behavior's maintaining reinforcers was
155. a prerequisite to the appropriate use of extinction
(unknown reinforcers cannot be withheld), it ap-
pears that an answer to the question "Is a functional
analysis of a behavior problem useful in developing
an effective treatment program?" can be provided
by way of data. This represents a significant im-
provement over other answers based on theory,
logic, or humane philosophy without direct em-
pirical evidence.
But extinction represents only one approach to
treatment. There is ample evidence in both the basic
and applied literature that punishment can override
the effects of reinforcement. However, almost all
studies involving the use of punishment to reduce
behavior problems contain a limitation noted pre-
viously: Administration of punishment is con-
founded with the termination of reinforcement. Ex-
tinction is relevant to a consideration of punishment
effects because, from the standpoint of methodol-
ogy, the suppressive properties of a punishing stim-
ulus should be evaluated while behavior is con-
currently reinforced, unless it can be shown first
that extinction alone does not reduce behavior. Such
an arrangement increases the likelihood that ob-
156. served reductions in behavior can be attributed to
punishment rather than to extinction, which seems
to be important as a justification for using punish-
ment over extinction. At the present time, it is
unclear that punishment so applied would have the
same suppressive effects as those typically reported
in the literature. This fact, in addition to the pos-
sibility that stimuli delivered as punishment could
function as reinforcement, underscores the relevance
of both functional analysis procedures and extinc-
tion controls to research on punishment.
With respect to reinforcement-based interven-
tions, the finding that arbitrary or irrelevant rein-
forcers-those that do not maintain the target be-
142
VARIATIONS OF EXTINCTION 143
havior-delivered in a DRO or DRA schedule
successfully competed with an intact baseline of
reinforcement for the behavior problem (i.e., the
157. target behavior still produced the maintaining re-
inforcer) argues against the necessity of identifying
the maintaining reinforcer. That is, if reinforcers
could be found that are different than but substi-
tutable for those maintaining the behavior problem,
the task involves merely finding powerful reinforc-
ers. Several studies on DRO as treatment for SIB
have shown that reinforcer substitutability can be
achieved (e.g., Corte, Wolf, & Locke, 1971; Cow-
dery, Iwata, & Pace, 1990), but results from other
studies indicate that reinforcers irrelevant to be-
havioral function do not always compete success-
fully with relevant ones (e.g., Carr & Durand,
1985). Thus, it appears that reinforcer substitut-
ability is possible under conditions that remain to
be identified at the present time (see Green & Freed,
1993, for a general review of the topic). Never-
theless, it seems that a search for those conditions
should include specification of the maintaining re-
inforcer for which another stimulus would serve as
substitute, and that the evaluation of substitution
effects should include an extinction control (see
Mazaleski et al., 1993, for an example of this
methodology).
158. Extinction alone is rarely recommended and per-
haps accounts for the fact that little research has
been conducted on extinction effects per se. In light
of the present results indicating that properly de-
signed extinction procedures can produce powerful
clinical effects, future research on the treatment of
severe behavior disorders should include more care-
ful consideration of extinction as an integral com-
ponent of intervention as well as a significant source
of confounding effects when evaluating both re-
inforcement- and punishment-based approaches to
treatment.
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Received March 12, 1993
Initial editorial decision May 4, 1993
Revisions received July 23, 1993; August 6, 1993
Final acceptance August 26, 1993
Action Editor, F. Charles Mace
Chapter 4: Clustering
I
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What is Cluster Analysis?
Finding groups of objects such that the objects in a group will
be similar (or related) to one another and different from (or
unrelated to) the objects in other groups
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Applications of Cluster Analysis
Understanding
Group related documents for browsing, group genes and
proteins that have similar functionality, or group stocks with
similar price fluctuations
Summarization
Reduce the size of large data sets
Clustering precipitation in Australia
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What is not Cluster Analysis?
Simple segmentation
169. Dividing students into different registration groups
alphabetically, by last name
Results of a query
Groupings are a result of an external specification
Clustering is a grouping of objects based on the data
Supervised classification
Have class label information
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Notion of a Cluster can be Ambiguous
173. Six Clusters
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Types of Clusterings
A clustering is a set of clusters
Important distinction between hierarchical and partitional sets
of clusters
Partitional Clustering
A division of data objects into non-overlapping subsets
(clusters) such that each data object is in exactly one subset
Hierarchical clustering
A set of nested clusters organized as a hierarchical tree
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Partitional Clustering
Original Points
A Partitional Clustering
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Hierarchical Clustering
Traditional Hierarchical Clustering
Non-traditional Hierarchical Clustering
Non-traditional Dendrogram
Traditional Dendrogram
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176. Other Distinctions Between Sets of Clusters
Exclusive versus non-exclusive
In non-exclusive clusterings, points may belong to multiple
clusters.
Can represent multiple classes or ‘border’ points
Fuzzy versus non-fuzzy
In fuzzy clustering, a point belongs to every cluster with some
weight between 0 and 1
Weights must sum to 1
Probabilistic clustering has similar characteristics
Partial versus complete
In some cases, we only want to cluster some of the data
Heterogeneous versus homogeneous
Clusters of widely different sizes, shapes, and densities
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Types of Clusters
Well-separated clusters
Center-based clusters
177. Contiguous clusters
Density-based clusters
Property or Conceptual
Described by an Objective Function
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Types of Clusters: Well-Separated
Well-Separated Clusters:
A cluster is a set of points such that any point in a cluster is
closer (or more similar) to every other point in the cluster than
to any point not in the cluster.
3 well-separated clusters
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Types of Clusters: Center-Based
Center-based
A cluster is a set of objects such that an object in a cluster is
closer to the “center” of a cluster, than to the center of any
other cluster
The center of a cluster is a centroid.
The average of all the points in the cluster is a medoid
4 center-based clusters
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Types of Clusters: Contiguity-Based
179. Contiguous Cluster (Nearest neighbor or Transitive)
A point in a cluster is closer (or more similar) to one or more
other points in the cluster than to any point not in the cluster.
8 contiguous clusters
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Types of Clusters: Density-Based
Density-based
A cluster is a dense region of points, which is separated by low-
180. density regions, from other regions of high density.
Used when the clusters are irregular or intertwined, and when
noise and outliers are present.
6 density-based clusters
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Types of Clusters: Conceptual Clusters
Shared Property or Conceptual Clusters
Finds clusters that share some common property or represent a
particular concept.
.
2 Overlapping Circles
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Types of Clusters: Objective Function
Clusters Defined by an Objective Function
Finds clusters that minimize or maximize an objective function.
Enumerate all possible ways of dividing the points into clusters
and evaluate the `goodness' of each potential set of clusters by
using the given objective function. (NP Hard)
Can have global or local objectives.
Hierarchical clustering algorithms typically have local
objectives
Partitional algorithms typically have global objectives
A variation of the global objective function approach is to fit
the data to a parameterized model.
Parameters for the model are determined from the data.
Mixture models assume that the data is a ‘mixture' of a number
of statistical distributions.
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Characteristics of the Input Data Are Important
Type of proximity or density measure
Central to clustering
Depends on data and application
Data characteristics that affect proximity and/or density are
Dimensionality
Sparseness
Attribute type
Special relationships in the data
For example, autocorrelation
Distribution of the data
Noise and Outliers
Often interfere with the operation of the clustering algorithm
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183. Clustering Algorithms
K-means and its variants
Hierarchical clustering
Density-based clustering
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K-means Clustering
Partitional clustering approach
Number of clusters, K, must be specified
Each cluster is associated with a centroid (center point)
Each point is assigned to the cluster with the closest centroid
The basic algorithm is very simple
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Example of K-means Clustering
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Example of K-means Clustering
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K-means Clustering – Details
Initial centroids are often chosen randomly.
Clusters produced vary from one run to another.
The centroid is (typically) the mean of the points in the cluster.
‘Closeness’ is measured by Euclidean distance, cosine
similarity, correlation, etc.
K-means will converge for common similarity measures
mentioned above.
Most of the convergence happens in the first few iterations.
Often the stopping condition is changed to ‘Until relatively few
points change clusters’
Complexity is O( n * K * I * d )
n = number of points, K = number of clusters,
I = number of iterations, d = number of attributes
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Evaluating K-means Clusters
Most common measure is Sum of Squared Error (SSE)
For each point, the error is the distance to the nearest cluster
To get SSE, we square these errors and sum them.
x is a data point in cluster Ci and mi is the representative point
for cluster Ci
can show that mi corresponds to the center (mean) of the
cluster
Given two sets of clusters, we prefer the one with the smallest
error
One easy way to reduce SSE is to increase K, the number of
clusters
A good clustering with smaller K can have a lower SSE than a
poor clustering with higher K
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Two different K-means Clusterings
Sub-optimal Clustering
Optimal Clustering
Original Points
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Limitations of K-means
K-means has problems when clusters are of differing
Sizes
Densities
Non-globular Shapes
K-means has problems when the data contains outliers/noise.
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Limitations of K-means: Differing Sizes
Original Points
K-means (3 Clusters)
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Limitations of K-means: Differing Density
189. Original Points
K-means (3 Clusters)
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Limitations of K-means: Non-globular Shapes
Original Points
K-means (2 Clusters)
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Overcoming K-means Limitations
190. Original PointsK-means Clusters
One solution is to use many clusters.
Find parts of clusters, but need to put together.
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Overcoming K-means Limitations
Original PointsK-means Clusters
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191. Overcoming K-means Limitations
Original PointsK-means Clusters
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Importance of Choosing Initial Centroids
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Importance of Choosing Initial Centroids
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Importance of Choosing Initial Centroids …
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Importance of Choosing Initial Centroids …
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Problems with Selecting Initial Points
If there are K ‘real’ clusters then the chance of selecting one
centroid from each cluster is small.
Chance is relatively small when K is large
If clusters are the same size, n, then
194. For example, if K = 10, then probability = 10!/1010 = 0.00036
Sometimes the initial centroids will readjust themselves in
‘right’ way, and sometimes they don’t
Consider an example of five pairs of clusters
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10 Clusters Example
Starting with two initial centroids in one cluster of each pair of
clusters
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195. 10 Clusters Example
Starting with two initial centroids in one cluster of each pair of
clusters
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