This document discusses different types of clustering methods used in data analysis. It covers partitioning methods like k-means and k-medoids that group data into a predefined number of clusters. It also describes different data types that can be clustered, including interval-scaled, binary, categorical, ordinal and ratio-scaled variables. The document provides details on calculating distances and similarities between objects for different variable types during clustering.
Step by step operations by which we make a group of objects in which attributes
of all the objects are nearly similar, known as clustering. So, a cluster is a collection of
objects that acquire nearly same attribute values. The property of an object in a cluster is
similar to other objects in same cluster but different with objects of other clusters.
Clustering is used in wide range of applications like pattern recognition, image processing,
data analysis, machine learning etc. Nowadays, more attention has been put on categorical
data rather than numerical data. Where, the range of numerical attributes organizes in a
class like small, medium, high, and so on. There is wide range of algorithm that used to
make clusters of given categorical data. Our approach is to enhance the working on well-
known clustering algorithm k-modes to improve accuracy of algorithm. We proposed a new
approach named “High Accuracy Clustering Algorithm for Categorical datasets”.
Unsupervised learning Algorithms and Assumptionsrefedey275
Topics :
Introduction to unsupervised learning
Unsupervised learning Algorithms and Assumptions
K-Means algorithm – introduction
Implementation of K-means algorithm
Hierarchical Clustering – need and importance of hierarchical clustering
Agglomerative Hierarchical Clustering
Working of dendrogram
Steps for implementation of AHC using Python
Gaussian Mixture Models – Introduction, importance and need of the model
Normal , Gaussian distribution
Implementation of Gaussian mixture model
Understand the different distance metrics used in clustering
Euclidean, Manhattan, Cosine, Mahala Nobis
Features of a Cluster – Labels, Centroids, Inertia, Eigen vectors and Eigen values
Principal component analysis
Supervised learning (classification)
Supervision: The training data (observations, measurements, etc.) are accompanied by labels indicating the class of the observations
New data is classified based on the training set
Unsupervised learning (clustering)
The class labels of training data is unknown
Given a set of measurements, observations, etc. with the aim of establishing the existence of classes or clusters in the data
Types of Hierarchical Clustering
There are mainly two types of hierarchical clustering:
Agglomerative hierarchical clustering
Divisive Hierarchical clustering
A distribution in statistics is a function that shows the possible values for a variable and how often they occur.
In probability theory and statistics, the Normal Distribution, also called the Gaussian Distribution.
is the most significant continuous probability distribution.
Sometimes it is also called a bell curve.
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.
This document provides a short review of clustering techniques for students. It defines clustering and different types of grouping methods such as hard vs soft clustering. It discusses popular clustering algorithms like hierarchical clustering, k-means clustering, and density-based clustering. It also covers cluster validity, usability, preprocessing techniques, meta methods, and visual clustering. Open problems in clustering mentioned include how to identify outlier objects and accelerate classification.
1. Singular Value Decomposition (SVD) is a matrix factorization technique that decomposes a matrix into three other matrices.
2. SVD is primarily used for dimensionality reduction, information extraction, and noise reduction.
3. Key applications of SVD include matrix approximation, principal component analysis, image compression, recommendation systems, and signal processing.
EDAB Module 5 Singular Value Decomposition (SVD).pptxrajalakshmi5921
1. Singular Value Decomposition (SVD) is a matrix factorization technique that decomposes a matrix into three other matrices.
2. SVD is primarily used for dimensionality reduction, information extraction, and noise reduction.
3. Key applications of SVD include matrix approximation, principal component analysis, image compression, recommendation systems, and signal processing.
This document discusses various clustering techniques used in data mining. It begins by defining clustering as an unsupervised learning technique that groups similar objects together. It then discusses advantages of clustering such as quality improvement and reuse opportunities. Several clustering methods are described such as K-means clustering, which aims to partition observations into k clusters where each observation belongs to the cluster with the nearest mean. The document concludes by discussing advantages of K-means clustering such as its linear time complexity and its use for spherical cluster shapes.
Step by step operations by which we make a group of objects in which attributes
of all the objects are nearly similar, known as clustering. So, a cluster is a collection of
objects that acquire nearly same attribute values. The property of an object in a cluster is
similar to other objects in same cluster but different with objects of other clusters.
Clustering is used in wide range of applications like pattern recognition, image processing,
data analysis, machine learning etc. Nowadays, more attention has been put on categorical
data rather than numerical data. Where, the range of numerical attributes organizes in a
class like small, medium, high, and so on. There is wide range of algorithm that used to
make clusters of given categorical data. Our approach is to enhance the working on well-
known clustering algorithm k-modes to improve accuracy of algorithm. We proposed a new
approach named “High Accuracy Clustering Algorithm for Categorical datasets”.
Unsupervised learning Algorithms and Assumptionsrefedey275
Topics :
Introduction to unsupervised learning
Unsupervised learning Algorithms and Assumptions
K-Means algorithm – introduction
Implementation of K-means algorithm
Hierarchical Clustering – need and importance of hierarchical clustering
Agglomerative Hierarchical Clustering
Working of dendrogram
Steps for implementation of AHC using Python
Gaussian Mixture Models – Introduction, importance and need of the model
Normal , Gaussian distribution
Implementation of Gaussian mixture model
Understand the different distance metrics used in clustering
Euclidean, Manhattan, Cosine, Mahala Nobis
Features of a Cluster – Labels, Centroids, Inertia, Eigen vectors and Eigen values
Principal component analysis
Supervised learning (classification)
Supervision: The training data (observations, measurements, etc.) are accompanied by labels indicating the class of the observations
New data is classified based on the training set
Unsupervised learning (clustering)
The class labels of training data is unknown
Given a set of measurements, observations, etc. with the aim of establishing the existence of classes or clusters in the data
Types of Hierarchical Clustering
There are mainly two types of hierarchical clustering:
Agglomerative hierarchical clustering
Divisive Hierarchical clustering
A distribution in statistics is a function that shows the possible values for a variable and how often they occur.
In probability theory and statistics, the Normal Distribution, also called the Gaussian Distribution.
is the most significant continuous probability distribution.
Sometimes it is also called a bell curve.
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.
This document provides a short review of clustering techniques for students. It defines clustering and different types of grouping methods such as hard vs soft clustering. It discusses popular clustering algorithms like hierarchical clustering, k-means clustering, and density-based clustering. It also covers cluster validity, usability, preprocessing techniques, meta methods, and visual clustering. Open problems in clustering mentioned include how to identify outlier objects and accelerate classification.
1. Singular Value Decomposition (SVD) is a matrix factorization technique that decomposes a matrix into three other matrices.
2. SVD is primarily used for dimensionality reduction, information extraction, and noise reduction.
3. Key applications of SVD include matrix approximation, principal component analysis, image compression, recommendation systems, and signal processing.
EDAB Module 5 Singular Value Decomposition (SVD).pptxrajalakshmi5921
1. Singular Value Decomposition (SVD) is a matrix factorization technique that decomposes a matrix into three other matrices.
2. SVD is primarily used for dimensionality reduction, information extraction, and noise reduction.
3. Key applications of SVD include matrix approximation, principal component analysis, image compression, recommendation systems, and signal processing.
This document discusses various clustering techniques used in data mining. It begins by defining clustering as an unsupervised learning technique that groups similar objects together. It then discusses advantages of clustering such as quality improvement and reuse opportunities. Several clustering methods are described such as K-means clustering, which aims to partition observations into k clusters where each observation belongs to the cluster with the nearest mean. The document concludes by discussing advantages of K-means clustering such as its linear time complexity and its use for spherical cluster shapes.
This document provides an introduction to cluster analysis, including definitions of key concepts, types of data and clusters, and clustering techniques. It defines cluster analysis as finding groups of similar objects that are different from objects in other groups. There are various types of clusters that can be formed, such as well-separated, center-based, contiguous, and density-based clusters. Common clustering techniques include partitional clustering (e.g., k-means), hierarchical clustering, and density-based clustering. The document discusses considerations for different data types and provides details on partitioning clustering algorithms.
Cluster analysis is an unsupervised machine learning technique that groups similar data objects into clusters. It finds internal structures within unlabeled data by partitioning it into groups based on similarity. Some key applications of cluster analysis include market segmentation, document classification, and identifying subtypes of diseases. The quality of clusters depends on both the similarity measure used and how well objects are grouped within each cluster versus across clusters.
This document provides an overview of different techniques for clustering categorical data. It discusses various clustering algorithms that have been used for categorical data, including K-modes, ROCK, COBWEB, and EM algorithms. It also reviews more recently developed algorithms for categorical data clustering, such as algorithms based on particle swarm optimization, rough set theory, and feature weighting schemes. The document concludes that clustering categorical data remains an important area of research, with opportunities to develop techniques that initialize cluster centers better.
This document provides an overview of cluster analysis techniques. It begins by defining cluster analysis and its applications. It then categorizes major clustering methods into partitioning methods (like k-means and k-medoids), hierarchical methods, density-based methods, grid-based methods, and model-based methods. The document discusses different data types that can be clustered and measures for determining cluster quality. It also outlines requirements for effective clustering in data mining.
UNIT 3: Data Warehousing and Data MiningNandakumar P
UNIT-III Classification and Prediction: Issues Regarding Classification and Prediction – Classification by Decision Tree Introduction – Bayesian Classification – Rule Based Classification – Classification by Back propagation – Support Vector Machines – Associative Classification – Lazy Learners – Other Classification Methods – Prediction – Accuracy and Error Measures – Evaluating the Accuracy of a Classifier or Predictor – Ensemble Methods – Model Section.
Data Mining StepsProblem Definition Market AnalysisCsharondabriggs
Data Mining Steps
Problem Definition
Market Analysis
Customer Profiling, Identifying Customer Requirements, Cross Market Analysis, Target Marketing, Determining Customer purchasing pattern
Corporate Analysis and Risk Management
Finance Planning and Asset Evaluation, Resource Planning, Competition
Fraud Detection
Customer Retention
Production Control
Science Exploration
> Data Preparation
Data preparation is about constructing a dataset from one or more data sources to be used for exploration and modeling. It is a solid practice to start with an initial dataset to get familiar with the data, to discover first insights into the data and have a good understanding of any possible data quality issues. The Datasets you are provided in these projects were obtained from kaggle.com.
Variable selection and description
Numerical – Ratio, Interval
Categorical – Ordinal, Nominal
Simplifying variables: From continuous to discrete
Formatting the data
Basic data integrity checks: missing data, outliers
> Data Exploration
Data Exploration is about describing the data by means of statistical and visualization techniques.
· Data Visualization:
o
Univariate
analysis explores variables (attributes) one by one. Variables could be either categorical or numerical.
Univariate Analysis - Categorical
Statistics
Visualization
Description
Count
Bar Chart
The number of values of the specified variable.
Count%
Pie Chart
The percentage of values of the specified variable
Univariate Analysis - Numerical
Statistics
Visualization
Equation
Description
Count
Histogram
N
The number of values (observations) of the variable.
Minimum
Box Plot
Min
The smallest value of the variable.
Maximum
Box Plot
Max
The largest value of the variable.
Mean
Box Plot
The sum of the values divided by the count.
Median
Box Plot
The middle value. Below and above median lies an equal number of values.
Mode
Histogram
The most frequent value. There can be more than one mode.
Quantile
Box Plot
A set of 'cut points' that divide a set of data into groups containing equal numbers of values (Quartile, Quintile, Percentile, ...).
Range
Box Plot
Max-Min
The difference between maximum and minimum.
Variance
Histogram
A measure of data dispersion.
Standard Deviation
Histogram
The square root of variance.
Coefficient of Deviation
Histogram
A measure of data dispersion divided by mean.
Skewness
Histogram
A measure of symmetry or asymmetry in the distribution of data.
Kurtosis
Histogram
A measure of whether the data are peaked or flat relative to a normal distribution.
Note: There are two types of numerical variables, interval and ratio. An interval variable has values whose differences are interpretable, but it does not have a true zero. A good example is temperature in Centigrade degrees. Data on an int ...
Clustering is an unsupervised learning technique used to group unlabeled data points into clusters based on similarity. It is widely used in data mining applications. The k-means algorithm is one of the simplest clustering algorithms that partitions data into k predefined clusters, where each data point belongs to the cluster with the nearest mean. It works by assigning data points to their closest cluster centroid and recalculating the centroids until clusters stabilize. The k-medoids algorithm is similar but uses actual data points as centroids instead of means, making it more robust to outliers.
This document provides an overview of clustering and classification techniques in data mining. It defines clustering and classification as unsupervised and supervised learning respectively. The document discusses how classification works by building a model from training data and then using the model to classify new data. For clustering, it explains that clusters are formed by grouping similar data objects without predefined labels. The document also describes different types of clustering techniques like hierarchical, partitioning, and probabilistic clustering. Finally, it provides a step-by-step explanation of the k-means clustering algorithm.
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.
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.
Read first few slides cluster analysisKritika Jain
Cluster analysis is a technique used to group similar objects together based on their characteristics. It involves calculating distances between objects to determine which ones are most similar and should be clustered together. There are hierarchical and non-hierarchical approaches to cluster analysis. Hierarchical clustering starts with each object in its own cluster and then combines the most similar clusters together in each step, while non-hierarchical clustering assigns objects directly to pre-specified clusters. A combination of the two methods is often best to determine the optimal number of clusters.
Cluster analysis is a technique used to group similar objects together based on their characteristics. It involves calculating distances between objects to determine which ones are most similar and should be clustered together. There are hierarchical and non-hierarchical approaches to cluster analysis. Hierarchical clustering starts with each object in its own cluster and then combines the most similar clusters together in each step, while non-hierarchical clustering assigns objects directly to pre-specified clusters. A combination of the two methods is often best to determine the optimal number of clusters.
Cluster analysis is a technique used to group similar objects together based on their characteristics. It involves calculating distances between objects to determine which ones are most similar and should be clustered together. There are hierarchical and non-hierarchical approaches to cluster analysis. Hierarchical clustering starts with each object in its own cluster and then combines the most similar clusters together in each step, while non-hierarchical clustering assigns objects directly to pre-specified clusters. A combination of the two methods is often best to determine the optimal number of clusters.
The document describes different types of clustering algorithms, including partitioning, hierarchical, density-based, and grid-based methods. Partitioning methods like k-means and k-medoids aim to partition objects into k clusters by optimizing an objective function. Hierarchical clustering builds a hierarchy of clusters based on distance, either through an agglomerative (bottom-up) or divisive (top-down) approach. Density-based methods identify clusters based on density rather than distance. Grid-based methods quantize the space into a finite number of cells that form a grid structure.
This document summarizes Chapter 10 of the book "Data Mining: Concepts and Techniques (3rd ed.)" which covers cluster analysis. The chapter introduces different types of clustering methods including partitioning methods like k-means and k-medoids, hierarchical methods, density-based methods, and grid-based methods. It discusses how to evaluate the quality of clustering results and highlights considerations for cluster analysis such as similarity measures, clustering space, and challenges like scalability and high dimensionality.
This document provides an overview of clustering and k-means clustering algorithms. It begins by defining clustering as the process of grouping similar objects together and dissimilar objects separately. K-means clustering is introduced as an algorithm that partitions data points into k clusters by minimizing total intra-cluster variance, iteratively updating cluster means. The k-means algorithm and an example are described in detail. Weaknesses and applications are discussed. Finally, vector quantization and principal component analysis are briefly introduced.
The document discusses different clustering methods including partitioning, hierarchical, density-based, and grid-based approaches. It provides details on popular partitioning algorithms like k-means and k-medoids, describing how they work, their strengths and weaknesses. Hierarchical clustering methods like AGNES and DIANA are also covered, including how distances between clusters are calculated during the merging or splitting process.
ViewShift: Hassle-free Dynamic Policy Enforcement for Every Data LakeWalaa Eldin Moustafa
Dynamic policy enforcement is becoming an increasingly important topic in today’s world where data privacy and compliance is a top priority for companies, individuals, and regulators alike. In these slides, we discuss how LinkedIn implements a powerful dynamic policy enforcement engine, called ViewShift, and integrates it within its data lake. We show the query engine architecture and how catalog implementations can automatically route table resolutions to compliance-enforcing SQL views. Such views have a set of very interesting properties: (1) They are auto-generated from declarative data annotations. (2) They respect user-level consent and preferences (3) They are context-aware, encoding a different set of transformations for different use cases (4) They are portable; while the SQL logic is only implemented in one SQL dialect, it is accessible in all engines.
#SQL #Views #Privacy #Compliance #DataLake
This document provides an introduction to cluster analysis, including definitions of key concepts, types of data and clusters, and clustering techniques. It defines cluster analysis as finding groups of similar objects that are different from objects in other groups. There are various types of clusters that can be formed, such as well-separated, center-based, contiguous, and density-based clusters. Common clustering techniques include partitional clustering (e.g., k-means), hierarchical clustering, and density-based clustering. The document discusses considerations for different data types and provides details on partitioning clustering algorithms.
Cluster analysis is an unsupervised machine learning technique that groups similar data objects into clusters. It finds internal structures within unlabeled data by partitioning it into groups based on similarity. Some key applications of cluster analysis include market segmentation, document classification, and identifying subtypes of diseases. The quality of clusters depends on both the similarity measure used and how well objects are grouped within each cluster versus across clusters.
This document provides an overview of different techniques for clustering categorical data. It discusses various clustering algorithms that have been used for categorical data, including K-modes, ROCK, COBWEB, and EM algorithms. It also reviews more recently developed algorithms for categorical data clustering, such as algorithms based on particle swarm optimization, rough set theory, and feature weighting schemes. The document concludes that clustering categorical data remains an important area of research, with opportunities to develop techniques that initialize cluster centers better.
This document provides an overview of cluster analysis techniques. It begins by defining cluster analysis and its applications. It then categorizes major clustering methods into partitioning methods (like k-means and k-medoids), hierarchical methods, density-based methods, grid-based methods, and model-based methods. The document discusses different data types that can be clustered and measures for determining cluster quality. It also outlines requirements for effective clustering in data mining.
UNIT 3: Data Warehousing and Data MiningNandakumar P
UNIT-III Classification and Prediction: Issues Regarding Classification and Prediction – Classification by Decision Tree Introduction – Bayesian Classification – Rule Based Classification – Classification by Back propagation – Support Vector Machines – Associative Classification – Lazy Learners – Other Classification Methods – Prediction – Accuracy and Error Measures – Evaluating the Accuracy of a Classifier or Predictor – Ensemble Methods – Model Section.
Data Mining StepsProblem Definition Market AnalysisCsharondabriggs
Data Mining Steps
Problem Definition
Market Analysis
Customer Profiling, Identifying Customer Requirements, Cross Market Analysis, Target Marketing, Determining Customer purchasing pattern
Corporate Analysis and Risk Management
Finance Planning and Asset Evaluation, Resource Planning, Competition
Fraud Detection
Customer Retention
Production Control
Science Exploration
> Data Preparation
Data preparation is about constructing a dataset from one or more data sources to be used for exploration and modeling. It is a solid practice to start with an initial dataset to get familiar with the data, to discover first insights into the data and have a good understanding of any possible data quality issues. The Datasets you are provided in these projects were obtained from kaggle.com.
Variable selection and description
Numerical – Ratio, Interval
Categorical – Ordinal, Nominal
Simplifying variables: From continuous to discrete
Formatting the data
Basic data integrity checks: missing data, outliers
> Data Exploration
Data Exploration is about describing the data by means of statistical and visualization techniques.
· Data Visualization:
o
Univariate
analysis explores variables (attributes) one by one. Variables could be either categorical or numerical.
Univariate Analysis - Categorical
Statistics
Visualization
Description
Count
Bar Chart
The number of values of the specified variable.
Count%
Pie Chart
The percentage of values of the specified variable
Univariate Analysis - Numerical
Statistics
Visualization
Equation
Description
Count
Histogram
N
The number of values (observations) of the variable.
Minimum
Box Plot
Min
The smallest value of the variable.
Maximum
Box Plot
Max
The largest value of the variable.
Mean
Box Plot
The sum of the values divided by the count.
Median
Box Plot
The middle value. Below and above median lies an equal number of values.
Mode
Histogram
The most frequent value. There can be more than one mode.
Quantile
Box Plot
A set of 'cut points' that divide a set of data into groups containing equal numbers of values (Quartile, Quintile, Percentile, ...).
Range
Box Plot
Max-Min
The difference between maximum and minimum.
Variance
Histogram
A measure of data dispersion.
Standard Deviation
Histogram
The square root of variance.
Coefficient of Deviation
Histogram
A measure of data dispersion divided by mean.
Skewness
Histogram
A measure of symmetry or asymmetry in the distribution of data.
Kurtosis
Histogram
A measure of whether the data are peaked or flat relative to a normal distribution.
Note: There are two types of numerical variables, interval and ratio. An interval variable has values whose differences are interpretable, but it does not have a true zero. A good example is temperature in Centigrade degrees. Data on an int ...
Clustering is an unsupervised learning technique used to group unlabeled data points into clusters based on similarity. It is widely used in data mining applications. The k-means algorithm is one of the simplest clustering algorithms that partitions data into k predefined clusters, where each data point belongs to the cluster with the nearest mean. It works by assigning data points to their closest cluster centroid and recalculating the centroids until clusters stabilize. The k-medoids algorithm is similar but uses actual data points as centroids instead of means, making it more robust to outliers.
This document provides an overview of clustering and classification techniques in data mining. It defines clustering and classification as unsupervised and supervised learning respectively. The document discusses how classification works by building a model from training data and then using the model to classify new data. For clustering, it explains that clusters are formed by grouping similar data objects without predefined labels. The document also describes different types of clustering techniques like hierarchical, partitioning, and probabilistic clustering. Finally, it provides a step-by-step explanation of the k-means clustering algorithm.
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.
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.
Read first few slides cluster analysisKritika Jain
Cluster analysis is a technique used to group similar objects together based on their characteristics. It involves calculating distances between objects to determine which ones are most similar and should be clustered together. There are hierarchical and non-hierarchical approaches to cluster analysis. Hierarchical clustering starts with each object in its own cluster and then combines the most similar clusters together in each step, while non-hierarchical clustering assigns objects directly to pre-specified clusters. A combination of the two methods is often best to determine the optimal number of clusters.
Cluster analysis is a technique used to group similar objects together based on their characteristics. It involves calculating distances between objects to determine which ones are most similar and should be clustered together. There are hierarchical and non-hierarchical approaches to cluster analysis. Hierarchical clustering starts with each object in its own cluster and then combines the most similar clusters together in each step, while non-hierarchical clustering assigns objects directly to pre-specified clusters. A combination of the two methods is often best to determine the optimal number of clusters.
Cluster analysis is a technique used to group similar objects together based on their characteristics. It involves calculating distances between objects to determine which ones are most similar and should be clustered together. There are hierarchical and non-hierarchical approaches to cluster analysis. Hierarchical clustering starts with each object in its own cluster and then combines the most similar clusters together in each step, while non-hierarchical clustering assigns objects directly to pre-specified clusters. A combination of the two methods is often best to determine the optimal number of clusters.
The document describes different types of clustering algorithms, including partitioning, hierarchical, density-based, and grid-based methods. Partitioning methods like k-means and k-medoids aim to partition objects into k clusters by optimizing an objective function. Hierarchical clustering builds a hierarchy of clusters based on distance, either through an agglomerative (bottom-up) or divisive (top-down) approach. Density-based methods identify clusters based on density rather than distance. Grid-based methods quantize the space into a finite number of cells that form a grid structure.
This document summarizes Chapter 10 of the book "Data Mining: Concepts and Techniques (3rd ed.)" which covers cluster analysis. The chapter introduces different types of clustering methods including partitioning methods like k-means and k-medoids, hierarchical methods, density-based methods, and grid-based methods. It discusses how to evaluate the quality of clustering results and highlights considerations for cluster analysis such as similarity measures, clustering space, and challenges like scalability and high dimensionality.
This document provides an overview of clustering and k-means clustering algorithms. It begins by defining clustering as the process of grouping similar objects together and dissimilar objects separately. K-means clustering is introduced as an algorithm that partitions data points into k clusters by minimizing total intra-cluster variance, iteratively updating cluster means. The k-means algorithm and an example are described in detail. Weaknesses and applications are discussed. Finally, vector quantization and principal component analysis are briefly introduced.
The document discusses different clustering methods including partitioning, hierarchical, density-based, and grid-based approaches. It provides details on popular partitioning algorithms like k-means and k-medoids, describing how they work, their strengths and weaknesses. Hierarchical clustering methods like AGNES and DIANA are also covered, including how distances between clusters are calculated during the merging or splitting process.
ViewShift: Hassle-free Dynamic Policy Enforcement for Every Data LakeWalaa Eldin Moustafa
Dynamic policy enforcement is becoming an increasingly important topic in today’s world where data privacy and compliance is a top priority for companies, individuals, and regulators alike. In these slides, we discuss how LinkedIn implements a powerful dynamic policy enforcement engine, called ViewShift, and integrates it within its data lake. We show the query engine architecture and how catalog implementations can automatically route table resolutions to compliance-enforcing SQL views. Such views have a set of very interesting properties: (1) They are auto-generated from declarative data annotations. (2) They respect user-level consent and preferences (3) They are context-aware, encoding a different set of transformations for different use cases (4) They are portable; while the SQL logic is only implemented in one SQL dialect, it is accessible in all engines.
#SQL #Views #Privacy #Compliance #DataLake
Learn SQL from basic queries to Advance queriesmanishkhaire30
Dive into the world of data analysis with our comprehensive guide on mastering SQL! This presentation offers a practical approach to learning SQL, focusing on real-world applications and hands-on practice. Whether you're a beginner or looking to sharpen your skills, this guide provides the tools you need to extract, analyze, and interpret data effectively.
Key Highlights:
Foundations of SQL: Understand the basics of SQL, including data retrieval, filtering, and aggregation.
Advanced Queries: Learn to craft complex queries to uncover deep insights from your data.
Data Trends and Patterns: Discover how to identify and interpret trends and patterns in your datasets.
Practical Examples: Follow step-by-step examples to apply SQL techniques in real-world scenarios.
Actionable Insights: Gain the skills to derive actionable insights that drive informed decision-making.
Join us on this journey to enhance your data analysis capabilities and unlock the full potential of SQL. Perfect for data enthusiasts, analysts, and anyone eager to harness the power of data!
#DataAnalysis #SQL #LearningSQL #DataInsights #DataScience #Analytics
06-04-2024 - NYC Tech Week - Discussion on Vector Databases, Unstructured Data and AI
Round table discussion of vector databases, unstructured data, ai, big data, real-time, robots and Milvus.
A lively discussion with NJ Gen AI Meetup Lead, Prasad and Procure.FYI's Co-Found
The Building Blocks of QuestDB, a Time Series Databasejavier ramirez
Talk Delivered at Valencia Codes Meetup 2024-06.
Traditionally, databases have treated timestamps just as another data type. However, when performing real-time analytics, timestamps should be first class citizens and we need rich time semantics to get the most out of our data. We also need to deal with ever growing datasets while keeping performant, which is as fun as it sounds.
It is no wonder time-series databases are now more popular than ever before. Join me in this session to learn about the internal architecture and building blocks of QuestDB, an open source time-series database designed for speed. We will also review a history of some of the changes we have gone over the past two years to deal with late and unordered data, non-blocking writes, read-replicas, or faster batch ingestion.
Global Situational Awareness of A.I. and where its headedvikram sood
You can see the future first in San Francisco.
Over the past year, the talk of the town has shifted from $10 billion compute clusters to $100 billion clusters to trillion-dollar clusters. Every six months another zero is added to the boardroom plans. Behind the scenes, there’s a fierce scramble to secure every power contract still available for the rest of the decade, every voltage transformer that can possibly be procured. American big business is gearing up to pour trillions of dollars into a long-unseen mobilization of American industrial might. By the end of the decade, American electricity production will have grown tens of percent; from the shale fields of Pennsylvania to the solar farms of Nevada, hundreds of millions of GPUs will hum.
The AGI race has begun. We are building machines that can think and reason. By 2025/26, these machines will outpace college graduates. By the end of the decade, they will be smarter than you or I; we will have superintelligence, in the true sense of the word. Along the way, national security forces not seen in half a century will be un-leashed, and before long, The Project will be on. If we’re lucky, we’ll be in an all-out race with the CCP; if we’re unlucky, an all-out war.
Everyone is now talking about AI, but few have the faintest glimmer of what is about to hit them. Nvidia analysts still think 2024 might be close to the peak. Mainstream pundits are stuck on the wilful blindness of “it’s just predicting the next word”. They see only hype and business-as-usual; at most they entertain another internet-scale technological change.
Before long, the world will wake up. But right now, there are perhaps a few hundred people, most of them in San Francisco and the AI labs, that have situational awareness. Through whatever peculiar forces of fate, I have found myself amongst them. A few years ago, these people were derided as crazy—but they trusted the trendlines, which allowed them to correctly predict the AI advances of the past few years. Whether these people are also right about the next few years remains to be seen. But these are very smart people—the smartest people I have ever met—and they are the ones building this technology. Perhaps they will be an odd footnote in history, or perhaps they will go down in history like Szilard and Oppenheimer and Teller. If they are seeing the future even close to correctly, we are in for a wild ride.
Let me tell you what we see.
Predictably Improve Your B2B Tech Company's Performance by Leveraging DataKiwi Creative
Harness the power of AI-backed reports, benchmarking and data analysis to predict trends and detect anomalies in your marketing efforts.
Peter Caputa, CEO at Databox, reveals how you can discover the strategies and tools to increase your growth rate (and margins!).
From metrics to track to data habits to pick up, enhance your reporting for powerful insights to improve your B2B tech company's marketing.
- - -
This is the webinar recording from the June 2024 HubSpot User Group (HUG) for B2B Technology USA.
Watch the video recording at https://youtu.be/5vjwGfPN9lw
Sign up for future HUG events at https://events.hubspot.com/b2b-technology-usa/
Codeless Generative AI Pipelines
(GenAI with Milvus)
https://ml.dssconf.pl/user.html#!/lecture/DSSML24-041a/rate
Discover the potential of real-time streaming in the context of GenAI as we delve into the intricacies of Apache NiFi and its capabilities. Learn how this tool can significantly simplify the data engineering workflow for GenAI applications, allowing you to focus on the creative aspects rather than the technical complexities. I will guide you through practical examples and use cases, showing the impact of automation on prompt building. From data ingestion to transformation and delivery, witness how Apache NiFi streamlines the entire pipeline, ensuring a smooth and hassle-free experience.
Timothy Spann
https://www.youtube.com/@FLaNK-Stack
https://medium.com/@tspann
https://www.datainmotion.dev/
milvus, unstructured data, vector database, zilliz, cloud, vectors, python, deep learning, generative ai, genai, nifi, kafka, flink, streaming, iot, edge
1. 20IT501 – Data Warehousing and
Data Mining
III Year / V Semester
2. UNIT IV - CLUSTERING AND
OUTLIER ANALYSIS
Cluster Analysis - Types of Data – Categorization of
Major Clustering Methods – K-means– Partitioning
Methods – Hierarchical Methods - Density-Based
Methods – Grid Based Methods – Model-Based
Clustering Methods – Clustering High Dimensional
Data – Constraint – Based Cluster Analysis –
Outlier Analysis
3. Introduction
Clustering is the process of grouping the data into classes or
clusters, so that objects within a cluster have high similarity
in comparison to one another but are very dissimilar to
objects in other clusters.
Dissimilarities are assessed based on the attribute values
describing the objects. Often, distance measures are used.
Clustering has its roots in many areas, including data
mining, statistics, biology, and machine learning.
4. Cluster Analysis
The process of grouping a set of physical or abstract objects
into classes of similar objects is called clustering.
A cluster is a collection of data objects that are similar to
one another within the same cluster.
In business, clustering can help marketers discover distinct
groups in their customer bases and characterize customer
groups based on purchasing patterns.
5. Cluster Analysis
Clustering is also called data segmentation in some
applications because clustering partitions large data sets into
groups according to their similarity.
Clustering can also be used for outlier detection, where
outliers (values that are “far away” from any cluster)
Applications of outlier detection include the detection of
credit card fraud and the monitoring of criminal activities in
electronic commerce.
6. Cluster Analysis
In machine learning, clustering is an example of
unsupervised learning.
Unlike classification, clustering and unsupervised
learning do not rely on predefined classes and
class-labeled training examples.
For this reason, clustering is a form of learning
by observation, rather than learning by examples.
7. Cluster Analysis
Requirements of clustering:
Scalability
Ability to deal with different types of attributes
Discovery of clusters with arbitrary shape
Minimal requirements for domain knowledge to
determine input parameters
Ability to deal with noisy data
8. Cluster Analysis
Requirements of clustering:
Incremental clustering and insensitivity to the
order of input records
High dimensionality
Constraint-based clustering
Interpretability and usability
9. Types of Data in Cluster Analysis
Interval-Scaled Variables:
It then describes distance measures that are commonly used for
computing the dissimilarity of objects described by such
variables. These measures include the Euclidean, Manhattan, and
Minkowski distances.
Interval-scaled variables are continuous measurements of a
roughly linear scale. Examples include weight and height,
latitude and longitude coordinates (e.g., when clustering houses),
and weather temperature
10. Types of Data in Cluster Analysis
Interval-Scaled Variables:
The measurement unit used can affect the clustering
analysis.
For example, changing measurement units from meters to
inches for height, or from kilograms to pounds for weight,
may lead to a very different clustering structure.
To help avoid dependence on the choice of measurement
units, the data should be standardized.
11. Types of Data in Cluster Analysis
Interval-Scaled Variables:
To standardize measurements, one choice is to convert
the original measurements to unitless variables.
Calculate the mean absolute deviation, sf :
Calculate the standardized measurement, or z-score:
12. Types of Data in Cluster Analysis
Interval-Scaled Variables:
The most popular distance measure is Euclidean
distance, which is defined as
Another well-known metric is Manhattan (or city
block) distance, defined as
13. Types of Data in Cluster Analysis
Interval-Scaled Variables:
14. Types of Data in Cluster Analysis
Binary Variables:
A binary variable has only two states: 0 or 1, where 0
means that the variable is absent, and 1 means that it is
present.
Treating binary variables as if they are interval-scaled
can lead to misleading clustering results. Therefore,
methods specific to binary data are necessary for
computing dissimilarities.
15. Types of Data in Cluster Analysis
Binary Variables:
A binary variable is symmetric if both of its states are
equally valuable and carry the same weight; that is, there is
no preference on which outcome should be coded as 0 or 1.
One such example could be the attribute gender having the
states male and female.
Its dissimilarity (or distance) measure
16. Types of Data in Cluster Analysis
Binary Variables:
A binary variable is asymmetric if the outcomes of the
states are not equally important, such as the positive
and negative outcomes of a disease test.
The dissimilarity based on such variables is called
asymmetric binary dissimilarity, where the number of
negative matches, t, is considered unimportant and
thus is ignored in the computation
17. Types of Data in Cluster Analysis
Binary Variables:
we can measure the distance between two binary
variables based on the notion of similarity instead of
dissimilarity.
For example, the asymmetric binary similarity
between the objects i and j, or sim(i, j), can be
computed as,
18. Types of Data in Cluster Analysis
Categorical Variables
A categorical variable is a generalization of the binary
variable in that it can take on more than two states.
For example, map color is a categorical variable that may
have, say, five states: red, yellow, green, pink, and blue.
The dissimilarity between two objects i and j can be
computed based on the ratio of mismatches:
19. Types of Data in Cluster Analysis
Ordinal Variables
A discrete ordinal variable resembles a categorical
variable, except that the M states of the ordinal value
are ordered in a meaningful sequence.
For example, professional ranks are often enumerated
in a sequential order, such as assistant, associate, and
full for professors
20. Types of Data in Cluster Analysis
Ordinal Variables
A continuous ordinal variable looks like a set of
continuous data of an unknown scale; that is, the
relative ordering of the values is essential but their
actual magnitude is not.
For example, the relative ranking in a particular sport
(e.g., gold, silver, bronze)
21. Types of Data in Cluster Analysis
Ratio-Scaled Variables
A ratio-scaled variable makes a positive
measurement on a nonlinear scale, such as an
exponential scale, approximately following the
formula AeBt or Ae-Bt
22. Types of Data in Cluster Analysis
Variables of Mixed Types
One approach is to group each kind of variable together,
performing a separate cluster analysis for each variable type.
This is feasible if these analyses derive compatible results.
A more preferable approach is to process all variable types
together, performing a single cluster analysis.
One such technique combines the different variables into a single
dissimilarity matrix, bringing all of the meaningful variables
onto a common scale of the interval [0.0,1.0].
23. Types of Data in Cluster Analysis
Vector Objects
In some applications, such as information retrieval,
text document clustering, and biological taxonomy, we
need to compare and cluster complex objects (such as
documents) containing a large number of symbolic
entities (such as keywords and phrases).
One popular way is to define the similarity function as
a cosine measure as follows:
24. Partitioning Methods
Given D, a data set of n objects, and k, the
number of clusters to form, a partitioning
algorithm organizes the objects into k partitions (k
≤ n), where each partition represents a cluster.
The objects within a cluster are “similar,” whereas
the objects of different clusters are “dissimilar” in
terms of the data set attributes.
25. Partitioning Methods
Centroid-Based Technique: The k-Means Method
The k-means algorithm takes the input parameter, k,
and partitions a set of n objects into k clusters so that
the resulting intracluster similarity is high but the
intercluster similarity is low.
Cluster similarity is measured in regard to the mean
value of the objects in a cluster, which can be viewed
as the cluster’s centroid or center of gravity.
26. Partitioning Methods
Centroid-Based Technique: The k-Means Method
Algorithm: k-means. The k-means algorithm for
partitioning, where each cluster’s center is represented
by the mean value of the objects in the cluster.
Input:
k: the number of clusters,
D: a data set containing n objects.
Output: A set of k clusters.
27. Partitioning Methods
Centroid-Based Technique: The k-Means Method
Method:
arbitrarily choose k objects from D as the initial cluster centers;
repeat
(re)assign each object to the cluster to which the object is the most
similar, based on the mean value of the objects in the cluster;
update the cluster means, i.e., calculate the mean value of the objects for
each cluster;
until no change;
28. Partitioning Methods
Representative Object-Based Technique: The
k-Medoids Method
The k-means algorithm is sensitive to outliers
because an object with an extremely large value
may substantially distort the distribution of data.
29. Partitioning Methods
PAM(Partitioning Around Medoids)
It attempts to determine k partitions for n objects.
After an initial random selection of k representative
objects, the algorithm repeatedly tries to make a better
choice of cluster representatives.
All of the possible pairs of objects are analyzed, where one
object in each pair is considered a representative object and
the other is not.
30. Partitioning Methods
PAM(Partitioning Around Medoids)
The quality of the resulting clustering is calculated for each such
combination.
An object, oj, is replaced with the object causing the greatest
reduction in error.
The set of best objects for each cluster in one iteration forms the
representative objects for the next iteration.
The final set of representative objects are the respective medoids
of the clusters.
31. Partitioning Methods
Which method is more robust—k-means or k-
medoids?
The k-medoids method is more robust than k-
means in the presence of noise and outliers.
A medoid is less influenced by outliers or other
extreme values than a mean.
32. Partitioning Methods
Partitioning Methods in Large Databases: From k-
Medoids to CLARANS
A typical k-medoids partitioning algorithm like PAM
works effectively for small data sets, but does not scale
well for large data sets.
To deal with larger data sets, a sampling-based method,
called CLARA (Clustering LARge Applications), can be
used
33. Partitioning Methods
Partitioning Methods in Large Databases: From k-
Medoids to CLARANS
Instead of taking the whole set of data into consideration, a
small portion of the actual data is chosen as a representative
of the data.
Medoids are then chosen from this sample using PAM.
If the sample is selected in a fairly random manner, it
should closely represent the original data set.
34. Partitioning Methods
Partitioning Methods in Large Databases: From k-Medoids to
CLARANS
The representative objects (medoids) chosen will likely be similar to
those that would have been chosen from the whole data set.
CLARA draws multiple samples of the data set, applies PAM on each
sample, and returns its best clustering as the output.
The complexity of each iteration now becomes O(ks2+k(n-k)), where s
is the size of the sample, k is the number of clusters, and n is the total
number of objects.
35. Partitioning Methods
Partitioning Methods in Large Databases: From
k-Medoids to CLARANS
The effectiveness of CLARA depends on the sample
size.
CLARA searches for the best k medoids among the
selected sample of the data set.
CLARA will never find the best clustering.
36. Hierarchical Methods
A hierarchical clustering method works by grouping data objects
into a tree of clusters.
Hierarchical clustering methods can be further classified as either
agglomerative or divisive, depending on whether the hierarchical
decomposition is formed in a bottom-up (merging) or top-down
(splitting) fashion.
The quality of a pure hierarchical clustering method suffers from its
inability to perform adjustment once a merge or split decision has
been executed.
37. Hierarchical Methods
Agglomerative and Divisive Hierarchical
Clustering:
Agglomerative hierarchical clustering: This bottom-up
strategy starts by placing each object in its own cluster
and then merges these atomic clusters into larger and
larger clusters, until all of the objects are in a single
cluster or until certain termination conditions are
satisfied.
38. Hierarchical Methods
Agglomerative and Divisive Hierarchical Clustering:
Divisive hierarchical clustering: This top-down strategy does
the reverse of agglomerative hierarchical clustering by starting
with all objects in one cluster.
It subdivides the cluster into smaller and smaller pieces, until
each object forms a cluster on its own or until it satisfies certain
termination conditions, such as a desired number of clusters is
obtained or the diameter of each cluster is within a certain
threshold.
40. Hierarchical Methods
Agglomerative and Divisive Hierarchical
Clustering:
A tree structure called a dendrogram is commonly
used to represent the process of hierarchical
clustering. It shows how objects are grouped
together step by step.
42. Hierarchical Methods
Agglomerative and Divisive Hierarchical
Clustering:
Four widely used measures for distance between
clusters are as follows, where |p-p’| is the distance
between two objects or points, p and p’; mi is the mean
for cluster, Ci; and ni is the number of objects in Ci.
44. Hierarchical Methods
Agglomerative and Divisive Hierarchical Clustering:
When an algorithm uses the minimum distance, dmin(Ci,
Cj), to measure the distance between clusters, it is
sometimes called a nearest-neighbor clustering algorithm.
When an algorithm uses the maximum distance, dmax(Ci,
Cj), to measure the distance between clusters, it is
sometimes called a farthest-neighbor clustering algorithm.
45. Hierarchical Methods
BIRCH: Balanced Iterative Reducing and Clustering Using
Hierarchies:
BIRCH is designed for clustering a large amount of numerical
data by integration of hierarchical clustering (at the initial
microclustering stage) and other clustering methods such as
iterative partitioning (at the later macroclustering stage).
It overcomes the two difficulties of agglomerative clustering
methods: (1) scalability and (2) the inability to undo what was
done in the previous step.
46. Hierarchical Methods
BIRCH: Balanced Iterative Reducing and Clustering Using
Hierarchies:
BIRCH introduces two concepts, clustering feature and
clustering feature tree (CF tree), which are used to summarize
cluster representations.
These structures help the clustering method achieve good speed
and scalability in large databases and also make it effective for
incremental and dynamic clustering of incoming objects.
47. Hierarchical Methods
BIRCH: Balanced Iterative Reducing and Clustering Using
Hierarchies:
A clustering feature (CF) is a three-dimensional vector
summarizing information about clusters of objects.
Given n d-dimensional objects or points in a cluster, {xi}, then
the CF of the cluster is defined as
CF=<n, LS, SS>
where n is the number of points in the cluster, LS is the linear sum
of the n points, and SS is the square sum of the data points
48. Hierarchical Methods
BIRCH: Balanced Iterative Reducing and
Clustering Using Hierarchies:
Clustering feature. Suppose that there are three points,
(2, 5), (3, 2), and (4, 3), in a cluster, C1. The clustering
feature of C1 is
CF1 = <3, (2+3+4,5+2+3); (22+32+42;52+22+32)> =
<3, (9,10), (29,38)>:
49. Hierarchical Methods
BIRCH: Balanced Iterative Reducing and Clustering Using
Hierarchies:
Clustering features are sufficient for calculating all of the
measurements that are needed for making clustering decisions in
BIRCH.
BIRCH thus utilizes storage efficiently by employing the
clustering features to summarize information about the clusters
of objects, thereby bypassing the need to store all objects.
50. Hierarchical Methods
BIRCH: Balanced Iterative Reducing and Clustering Using
Hierarchies:
A CF tree is a height-balanced tree that stores the clustering features
for a hierarchical clustering.
A CF tree has two parameters: branching factor, B, and threshold, T.
The branching factor specifies the maximum number of children per
nonleaf node.
The threshold parameter specifies the maximum diameter of
subclusters stored at the leaf nodes of the tree.
51. Hierarchical Methods
BIRCH: Balanced Iterative Reducing and
Clustering Using Hierarchies:
The computation complexity of the algorithm is O(n),
where n is the number of objects to be clustered.
Each node in a CF tree can hold only a limited
number of entries due to its size,
52. Hierarchical Methods
ROCK: A Hierarchical Clustering Algorithm for
Categorical Attributes
ROCK (RObust Clustering using linKs)
It explores the concept of links (the number of common
neighbors between two objects) for data with categorical
attributes.
Distance measures cannot lead to high-quality clusters
when clustering categorical data.
53. Hierarchical Methods
ROCK: A Hierarchical Clustering Algorithm for
Categorical Attributes
ROCK takes a more global approach to clustering by
considering the neighborhoods of individual pairs of points.
If two similar points also have similar neighborhoods, then
the two points likely belong to the same cluster and so can
be merged.
54. Hierarchical Methods
ROCK: A Hierarchical Clustering Algorithm for
Categorical Attributes
Based on these ideas, ROCK first constructs a sparse graph
from a given data similarity matrix using a similarity
threshold and the concept of shared neighbors.
It then performs agglomerative hierarchical clustering on
the sparse graph.
Random sampling is used for scaling up to large data sets.
55. Hierarchical Methods
Chameleon: A Hierarchical Clustering Algorithm
Using Dynamic Modeling
Chameleon is a hierarchical clustering algorithm that uses
dynamic modeling to determine the similarity between
pairs of clusters.
In Chameleon, cluster similarity is assessed based on how
well-connected objects are within a cluster and on the
proximity of clusters.
56. Hierarchical Methods
Chameleon: A Hierarchical Clustering Algorithm
Using Dynamic Modeling
That is, two clusters are merged if their
interconnectivity is high and they are close together.
The merge process facilitates the discovery of natural
and homogeneous clusters and applies to all types of
data as long as a similarity function can be specified.
58. Hierarchical Methods
Chameleon: A Hierarchical Clustering Algorithm
Using Dynamic Modeling
Chameleon uses a k-nearest-neighbor graph approach
to construct a sparse graph, where each vertex of the
graph represents a data object, and there exists an edge
between two vertices (objects) if one object is among
the k-most-similar objects of the other.
59. Hierarchical Methods
Chameleon: A Hierarchical Clustering Algorithm Using
Dynamic Modeling
The edges are weighted to reflect the similarity between objects.
It then uses an agglomerative hierarchical clustering algorithm
that repeatedly merges subclusters based on their similarity
To determine the pairs of most similar subclusters, it takes into
account both the interconnectivity as well as the closeness of the
clusters.
60. Hierarchical Methods
Chameleon: A Hierarchical Clustering
Algorithm Using Dynamic Modeling
Chameleon determines the similarity between
each pair of clusters Ci and Cj according to their
relative interconnectivity, RI(Ci, Cj), and their
relative closeness, RC(Ci, Cj)
61. Hierarchical Methods
Chameleon: A Hierarchical Clustering Algorithm
Using Dynamic Modeling
The relative interconnectivity, RI(Ci, Cj), between
two clusters, Ci and Cj, is defined as the absolute
interconnectivity between Ci and Cj, normalized with
respect to the internal interconnectivity of the two
clusters, Ci and Cj. That is,
62. Hierarchical Methods
Chameleon: A Hierarchical Clustering Algorithm
Using Dynamic Modeling
The relative closeness, RC(Ci, Cj), between a pair of
clusters,Ci and Cj, is the absolute closeness between
Ci and Cj, normalized with respect to the internal
closeness of the two clusters, Ci and Cj. It is defined as
63. Density-Based Methods
To discover clusters with arbitrary shape, density-
based clustering methods have been developed.
These typically regard clusters as dense regions
of objects in the data space that are separated by
regions of low density (representing noise).
64. Density-Based Methods
DBSCAN: A Density-Based Clustering Method Based on
Connected Regions with Sufficiently High Density
DBSCAN (Density-Based Spatial Clustering of Applications
with Noise)
The algorithm grows regions with sufficiently high density into
clusters and discovers clusters of arbitrary shape in spatial
databases with noise.
It defines a cluster as a maximal set of density-connected points.
65. Density-Based Methods
DBSCAN: A Density-Based Clustering Method Based
on Connected Regions with Sufficiently High Density
The neighborhood within a radius of a given object is
called the -neighborhood of the object.
If the -neighborhood of an object contains at least a
minimum number, MinPts, of objects, then the object is
called a core object.
66. Density-Based Methods
DBSCAN: A Density-Based Clustering Method
Based on Connected Regions with Sufficiently
High Density
Given a set of objects, D, we say that an object p is
directly density-reachable from object q if p is within
the e-neighborhood of q, and q is a core object.
67. Density-Based Methods
DBSCAN: A Density-Based Clustering Method Based
on Connected Regions with Sufficiently High Density
Direct density reachable: A point is called direct density
reachable if it has a core point in its neighbourhood.
Consider the point (1, 2), it has a core point (1.2, 2.5) in its
neighbourhood, hence, it will be a direct density reachable
point.
68. Density-Based Methods
DBSCAN: A Density-Based Clustering Method Based
on Connected Regions with Sufficiently High Density
Density Reachable: A point is called density reachable
from another point if they are connected through a series of
core points. For example, consider the points (1, 3) and
(1.5, 2.5), since they are connected through a core point
(1.2, 2.5), they are called density reachable from each
other.
69. Density-Based Methods
DBSCAN: A Density-Based Clustering Method Based on
Connected Regions with Sufficiently High Density
DBSCAN searches for clusters by checking the -neighborhood of
each point in the database.
If the -neighborhood of a point p contains more than MinPts, a new
cluster with p as a core object is created.
DBSCAN then iteratively collects directly density-reachable objects
from these core objects, which may involve the merge of a few density-
reachable clusters.
The process terminates when no new point can be added to any cluster.
71. Density-Based Methods
DBSCAN: A Density-Based Clustering Method Based
on Connected Regions with Sufficiently High Density
DBSCAN searches for clusters by checking the -
neighborhood of each point in the database.
If the -neighborhood of a point p contains more than
MinPts, a new cluster with p as a core object is created.
72. Density-Based Methods
DBSCAN: A Density-Based Clustering Method Based
on Connected Regions with Sufficiently High Density
DBSCAN then iteratively collects directly density-
reachable objects from these core objects, which may
involve the merge of a few density-reachable clusters.
The process terminates when no new point can be added to
any cluster.
73. Density-Based Methods
DBSCAN: A Density-Based Clustering Method
Based on Connected Regions with Sufficiently
High Density
If a spatial index is used, the computational
complexity of DBSCAN is O(nlogn), where n is the
number of database objects.
Otherwise, it is O(n2).
74. Density-Based Methods
OPTICS: Ordering Points to Identify the Clustering Structure
OPTICS computes an augmented cluster ordering for automatic and
interactive cluster analysis.
This ordering represents the density-based clustering structure of the
data.
It contains information that is equivalent to density-based clustering
obtained from a wide range of parameter settings.
The cluster ordering can be used to extract basic clustering information
(such as cluster centers or arbitrary-shaped clusters) as well as provide
the intrinsic clustering structure.
75. Density-Based Methods
OPTICS: Ordering Points to Identify the
Clustering Structure
The core-distance of an object p is the smallest ’
value that makes {p} a core object. If p is not a
core object, the core-distance of p is undefined.
77. Density-Based Methods
OPTICS: Ordering Points to Identify the Clustering
Structure
The reachability-distance of an object q with respect to
another object p is the greater value of the core-distance of
p and the Euclidean distance between p and q.
If p is not a core object, the reachability-distance between p
and q is undefined.
78. Density-Based Methods
OPTICS: Ordering Points to Identify the Clustering
Structure
An algorithm was proposed to extract clusters based on the
ordering information produced by OPTICS.
Such information is sufficient for the extraction of all
density-based clusterings with respect to any distance ’
that is smaller than the distance e used in generating the
order.
79. Density-Based Methods
OPTICS: Ordering Points to Identify the
Clustering Structure
Because of the structural equivalence of the OPTICS
algorithm to DBSCAN, the OPTICS algorithm has the
same runtime complexity as that of DBSCAN, that is,
O(nlogn) if a spatial index is used, where n is the
number of objects.
80. Density-Based Methods
OPTICS: Ordering Points to Identify the
Clustering Structure
Because of the structural equivalence of the OPTICS
algorithm to DBSCAN, the OPTICS algorithm has the
same runtime complexity as that of DBSCAN, that is,
O(nlogn) if a spatial index is used, where n is the
number of objects.
81. Density-Based Methods
DENCLUE: Clustering Based on Density Distribution Functions
DENCLUE (DENsity-based CLUstEring)
The method is built on the following ideas: the influence of each data point can
be formally modeled using a mathematical function, called an influence
function, which describes the impact of a data point within its neighborhood;
The overall density of the data space can be modeled analytically as the sum of
the influence function applied to all data points; and
Clusters can then be determined mathematically by identifying density
attractors, where density attractors are local maxima of the overall density
function.
82. Density-Based Methods
DENCLUE: Clustering Based on Density Distribution
Functions
The influence function of data object y on x is a function,
the influence function can be an arbitrary function that can be
determined by the distance between two objects in a
neighborhood.
The distance function, d(x, y), should be reflexive and
symmetric, such as the Euclidean distance function
83. Density-Based Methods
DENCLUE: Clustering Based on Density
Distribution Functions
The density function at an object or point x € Fd is
defined as the sum of influence functions of all
data points.
84. Density-Based Methods
DENCLUE: Clustering Based on Density Distribution
Functions
From the density function, we can define the gradient of
the function and the density attractor, the local maxima of
the overall density function.
An arbitrary-shape cluster for a set of density attractors is a
set of Cs, each being density-attracted to its respective
density attractor
85. Grid-Based Methods
The grid-based clustering approach uses a
multiresolution grid data structure.
It quantizes the object space into a finite number
of cells that form a grid structure on which all of
the operations for clustering are performed.
The main advantage of the approach is its fast
processing time
86. Grid-Based Methods
STING: STatistical INformation Grid
STING is a grid-based multiresolution clustering technique
in which the spatial area is divided into rectangular cells.
There are usually several levels of such rectangular cells
corresponding to different levels of resolution, and these
cells form a hierarchical structure: each cell at a high level
is partitioned to form a number of cells at the next lower
level.
87. Grid-Based Methods
STING: STatistical INformation Grid
Statistical information regarding the attributes in
each grid cell (such as the mean, maximum, and
minimum values) is precomputed and stored.
These statistical parameters are useful for query
processing
89. Grid-Based Methods
STING: STatistical INformation Grid
Statistical parameters of higher-level cells can easily be
computed from the parameters of the lower-level cells.
These parameters include the following: the attribute-
independent parameter, count; the attribute-dependent
parameters, mean, stdev (standard deviation), min (minimum),
max (maximum); and the type of distribution that the attribute
value in the cell follows, such as normal, uniform, exponential,
or none.
90. Grid-Based Methods
STING: STatistical INformation Grid
When the data are loaded into the database, the
parameters count, mean, stdev, min, and max of the
bottom-level cells are calculated directly from the data.
The value of distribution may either be assigned by the
user if the distribution type is known beforehand or
obtained by hypothesis tests such as the 2 test.
91. Grid-Based Methods
STING: STatistical INformation Grid
The type of distribution of a higher-level cell can be
computed based on the majority of distribution types
of its corresponding lower-level cells in conjunction
with a threshold filtering process.
If the distributions of the lower level cells disagree
with each other and fail the threshold test, the
distribution type of the high-level cell is set to none.
92. Grid-Based Methods
STING: STatistical INformation Grid
First, a layer within the hierarchical structure is
determined from which the query-answering process is
to start.
This layer typically contains a small number of cells.
For each cell in the current layer, we compute the
confidence interval (or estimated range of probability)
reflecting the cell’s relevancy to the given query.
93. Grid-Based Methods
STING: STatistical INformation Grid
The irrelevant cells are removed from further consideration.
Processing of the next lower level examines only the remaining
relevant cells. This process is repeated until the bottom layer is reached.
At this time, if the query specification is met, the regions of relevant
cells that satisfy the query are returned.
Otherwise, the data that fall into the relevant cells are retrieved and
further processed until they meet the requirements of the query.
94. Grid-Based Methods
STING: STatistical INformation Grid
The grid-based computation is query-independent,
because the statistical information stored in each cell
represents the summary information of the data in the
grid cell, independent of the query;
The grid structure facilitates parallel processing and
incremental updating
95. Grid-Based Methods
WaveCluster: Clustering Using Wavelet
Transformation
WaveCluster is a multiresolution clustering algorithm that
first summarizes the data by imposing a multidimensional
grid structure onto the data space.
It then uses a wavelet transformation to transform the
original feature space, finding dense regions in the
transformed space.
96. Grid-Based Methods
WaveCluster: Clustering Using Wavelet
Transformation
In this approach, each grid cell summarizes the
information of a group of points that map into the cell.
This summary information typically fits into main
memory for use by the multiresolution wavelet
transform and the subsequent cluster analysis.
97. Grid-Based Methods
WaveCluster: Clustering Using Wavelet Transformation
A wavelet transform is a signal processing technique that
decomposes a signal into different frequency subbands.
The wavelet model can be applied to d-dimensional signals by
applying a one-dimensional wavelet transform d times.
In applying a wavelet transform, data are transformed so as to
preserve the relative distance between objects at different levels
of resolution.
98. Grid-Based Methods
WaveCluster: Clustering Using Wavelet
Transformation
It provides unsupervised clustering
The multiresolution property of wavelet transformations
can help detect clusters at varying levels of accuracy.
Wavelet-based clustering is very fast, with a computational
complexity of O(n)
99. Model-Based Clustering Methods
Model-based clustering methods attempt to
optimize the fit between the given data and
some mathematical model.
Expectation-Maximization
Conceptual Clustering
Neural Network Approach
100. Model-Based Clustering Methods
Expectation-Maximization
Each cluster can be represented mathematically by a parametric
probability distribution.
The entire data is a mixture of these distributions, where each
individual distribution is typically referred to as a component
distribution.
The EM(Expectation-Maximization) algorithm is a popular
iterative refinement algorithm that can be used for finding the
parameter estimates.
101. Model-Based Clustering Methods
Expectation-Maximization
It can be viewed as an extension of the k-means
paradigm, which assigns an object to the cluster with
which it is most similar, based on the cluster mean.
Instead of assigning each object to a dedicated cluster,
EM assigns each object to a cluster according to a
weight representing the probability of membership.
102. Model-Based Clustering Methods
Expectation-Maximization – Algorithm:
Make an initial guess of the parameter vector: This
involves randomly selecting k objects to represent the
cluster means or centers (as in k-means partitioning),
as well as making guesses for the additional
parameters.
Iteratively refine the parameters (or clusters)
103. Model-Based Clustering Methods
Conceptual Clustering
A set of unlabeled objects, produces a classification
scheme over the objects.
Finding characteristic descriptions for each group,
where each group represents a concept or class.
Conceptual clustering is a two-step process: clustering
is performed first, followed by characterization.
104. Model-Based Clustering Methods
Conceptual Clustering – Classification Tree:
Each node in a classification tree refers to a concept
and contains a probabilistic description of that concept,
which summarizes the objects classified under the
node.
The sibling nodes at a given level of a classification
tree are said to form a partition.
105. Model-Based Clustering Methods
Conceptual Clustering – Classification Tree:
To classify an object using a classification tree, a
partial matching function is employed to descend
the tree along a path of “best” matching nodes.
107. Model-Based Clustering Methods
Neural Network Approach:
The neural network approach is motivated by
biological neural networks.
A neural network is a set of connected
input/output units, where each connection has a
weight associated with it.
108. Model-Based Clustering Methods
Neural Network Approach:
First, neural networks are inherently parallel and
distributed processing architectures.
Second, neural networks learn by adjusting their
interconnection weights so as to best fit the data.
Third, neural networks process numerical vectors and
require object patterns to be represented by quantitative
features only.
109. Clustering High-Dimensional Data
Most clustering methods are designed for clustering low-
dimensional data and encounter challenges when the dimensionality
of the data grows really high.
When dimensionality increases, data usually become increasingly
sparse because the data points are likely located in different
dimensional subspaces.
To overcome this difficulty, we may consider using feature (or
attribute) transformation and feature (or attribute) selection
techniques
110. Clustering High-Dimensional Data
Feature transformation methods:
Transform the data onto a smaller space
They summarize data by creating linear combinations
of the attributes, and may discover hidden structures in
the data.
Techniques do not actually remove any of the original
attributes from analysis.
111. Clustering High-Dimensional Data
Feature transformation methods:
This is problematic when there are a large number of
irrelevant attributes.
The transformed features (attributes) are often difficult to
interpret, making the clustering results less useful.
Feature transformation is only suited to data sets where
most of the dimensions are relevant to the clustering task.
112. Clustering High-Dimensional Data
Feature transformation methods:
Attribute subset selection (or feature subset selection)
is commonly used for data reduction by removing
irrelevant or redundant dimensions (or attributes).
It is most commonly performed by supervised
learning—the most relevant set of attributes are found
with respect to the given class labels
113. Clustering High-Dimensional Data
Feature transformation methods:
Subspace clustering is an extension to attribute
subset selection.
Subspace clustering searches for groups of
clusters within different subspaces of the same data
set.
114. Clustering High-Dimensional Data
CLIQUE: A Dimension-Growth Subspace Clustering
Method
CLIQUE (CLustering In QUEst)
The clustering process starts at single-dimensional
subspaces and grows upward to higher-dimensional ones.
Because CLIQUE partitions each dimension like a grid
structure and determines whether a cell is dense based on
the number of points it contains
115. Clustering High-Dimensional Data
CLIQUE: A Dimension-Growth Subspace
Clustering Method
An integration of density-based and grid-based
clustering methods.
116. Clustering High-Dimensional Data
CLIQUE: A Dimension-Growth Subspace Clustering
Method – Ideas:
Given a large set of multidimensional data points, the data space
is usually not uniformly occupied by the data points. CLIQUE’s
clustering identifies the sparse and the “crowded” areas in space
(or units), thereby discovering the overall distribution patterns of
the data set.
In CLIQUE, a cluster is defined as a maximal set of connected
dense units.
117. Clustering High-Dimensional Data
How does CLIQUE work?
In the first step, CLIQUE partitions the d-dimensional
data space into non-overlapping rectangular units,
identifying the dense units among these. This is done
(in 1-D) for each dimension.
In the second step, For each cluster, it determines the
maximal region that covers the cluster of connected
dense units.
118. Clustering High-Dimensional Data
PROCLUS: A Dimension-Reduction Subspace
Clustering Method:
PROCLUS (PROjected CLUStering)
It starts by finding an initial approximation of the clusters
in the high-dimensional attribute space.
Each dimension is then assigned a weight for each cluster,
and the updated weights are used in the next iteration to
regenerate the clusters.
119. Clustering High-Dimensional Data
PROCLUS: A Dimension-Reduction Subspace
Clustering Method:
It adopts a distance measure called Manhattan
segmental distance, which is the Manhattan distance
on a set of relevant dimensions.
The PROCLUS algorithm consists of three phases:
initialization, iteration, and cluster refinement.
120. Clustering High-Dimensional Data
PROCLUS: A Dimension-Reduction Subspace
Clustering Method:
In the initialization phase, it ensures that each cluster is
represented by at least one object in the selected set.
The iteration phase selects a random set of k medoids from
this reduced set (of medoids), and replaces “bad” medoids
with randomly chosen new medoids if the clustering is
improved.
121. Clustering High-Dimensional Data
PROCLUS: A Dimension-Reduction
Subspace Clustering Method:
The refinement phase computes new dimensions
for each medoid based on the clusters found,
reassigns points to medoids, and removes outliers.
122. Clustering High-Dimensional Data
Frequent Pattern–Based Clustering Methods
It searches for patterns (such as sets of items or
objects) that occur frequently in large data sets.
Frequent pattern mining can lead to the discovery
of interesting associations and correlations among
data objects.
123. Clustering High-Dimensional Data
Frequent Pattern–Based Clustering Methods - Frequent
term–based text clustering:
Text documents are clustered based on the frequent terms
they contain.
A term is any sequence of characters separated from other
terms by a delimiter.
A term can be made up of a single word or several words.
124. Clustering High-Dimensional Data
Frequent Pattern–Based Clustering Methods -
Frequent term–based text clustering:
In general, we first remove nontext information
(such as HTML tags and punctuation) and stop
words. Terms are then extracted.
125. Constraint-Based Cluster Analysis
Constraint-based clustering finds clusters that satisfy
user-specified preferences or constraints.
Constraints on individual objects: We can specify
constraints on the objects to be clustered.
In a real estate application, for example, one may like to
spatially cluster only those luxury mansions worth over a
million dollars.
This constraint confines the set of objects to be clustered.
126. Constraint-Based Cluster Analysis
Constraints on the selection of clustering parameters:
Clustering parameters are usually quite specific to the
given clustering algorithm.
Examples of parameters include k, the desired number of
clusters in a k-means algorithm; or e (the radius) and
MinPts (the minimum number of points) in the DBSCAN
algorithm.
127. Constraint-Based Cluster Analysis
Constraints on the selection of clustering
parameters:
Although such user-specified parameters may
strongly influence the clustering results, they are
usually confined to the algorithm itself.
128. Constraint-Based Cluster Analysis
Constraints on distance or similarity functions:
We can specify different distance or similarity
functions for specific attributes of the objects to be
clustered, or different distance measures for specific
pairs of objects.
When clustering sportsmen, for example, we may use
different weighting schemes for height, body weight,
age, and skill level.
129. Constraint-Based Cluster Analysis
User-specified constraints on the properties of
individual clusters:
A user may like to specify desired characteristics
of the resulting clusters, which may strongly
influence the clustering process.
130. Outlier Analysis
There exist data objects that do not comply
with the general behavior or model of the data.
Such data objects, which are grossly different
from or inconsistent with the remaining set of
data, are called outliers.
131. Outlier Analysis
Data visualization methods are weak in
detecting outliers in data with many
categorical attributes or in data of high
dimensionality, since human eyes are good at
visualizing numeric data of only two to three
dimensions.
132. Outlier Analysis
There are two basic types of procedures for detecting outliers:
Block procedures: In this case, either all of the suspect objects are
treated as outliers or all of them are accepted as consistent.
Consecutive (or sequential) procedures: An example of such a
procedure is the inside out procedure. Its main idea is that the object
that is least “likely” to be an outlier is tested first. If it is found to be an
outlier, then all of the more extreme values are also considered outliers;
otherwise, the next most extreme object is tested, and so on. This
procedure tends to be more effective than block procedures.
133. Outlier Analysis
How effective is the statistical approach at outlier
detection?
A major drawback is that most tests are for single attributes, yet
many data mining problems require finding outliers in
multidimensional space.
Statistical methods do not guarantee that all outliers will be
found for the cases where no specific test was developed, or
where the observed distribution cannot be adequately modeled
with any standard distribution.