The document presents an algorithm for k-medoid clustering based on Ant Colony Optimization (ACO) called ACO-MEDOIDS. It first provides background on data mining, clustering, and related clustering algorithms such as k-means and k-medoids. It then describes how ACO is adapted to solve the k-medoid clustering problem by using ants to explore the search space and iteratively update pheromone trails to find an optimal set of medoids, or cluster representative points. The ACO-MEDOIDS algorithm aims to address some limitations of traditional k-medoid clustering.
Cluster analysis is a technique used to group objects into clusters based on similarities. There are several major approaches to cluster analysis including partitioning methods, hierarchy methods, density-based methods, and grid-based methods. Partitioning methods construct partitions of the data objects into a set number of clusters by optimizing a chosen criterion, such as k-means and k-medoids clustering algorithms.
Building a Classifier Employing Prism Algorithm with Fuzzy LogicIJDKP
Classification in data mining is receiving immense interest in recent times. As the knowledge is based on
historical data, classifications of data are essential for discovering the knowledge. To decrease the
classification complexity, the quantitative attributes of data need splitting. But the splitting using the
classical logic is less accurate. This can be overcome by the use of fuzzy logic. This paper illustrates how to
build up the classification rules using the fuzzy logic. The fuzzy classifier is built on by using the prism
decision tree algorithm. This classifier produces more realistic results than the classical one. The
effectiveness of this method is justified over a sample dataset.
This document discusses cluster analysis and various clustering algorithms. It begins with an overview of supervised and unsupervised learning, as well as generative models. It then discusses 5 common clustering techniques: partitioning, hierarchical, density-based, grid-based, and model-based clustering. The document also covers challenges with cluster analysis such as centroid initialization, outlier handling, categorical data, the curse of dimensionality, and computational complexity. Specific clustering algorithms discussed in more detail include K-means, K-medoids, K-modes, mini-batch K-means, and scalable K-means++.
The document discusses different clustering techniques used for grouping large amounts of data. It covers partitioning methods like k-means and k-medoids that organize data into exclusive groups. It also describes hierarchical methods like agglomerative and divisive clustering that arrange data into nested groups or trees. Additionally, it mentions density-based and grid-based clustering and provides algorithms for different clustering approaches.
Cluster analysis is an unsupervised machine learning technique that groups unlabeled data points into clusters. The goal is to categorize data objects such that objects within a cluster are as similar as possible to each other, and as dissimilar as possible to objects in other clusters. Good clustering produces high quality clusters with high intra-class similarity and low inter-class similarity. Clustering has applications in marketing, land use analysis, insurance, and other domains.
Cluster analysis is an unsupervised learning technique that groups similar data objects into clusters. It finds internal structures within unlabeled data by grouping objects based on their characteristics. Clustering is used to gain insight into data distribution and as a preprocessing step for other algorithms. Some applications of clustering include marketing, land use analysis, insurance risk assessment, and city planning. The quality of clustering depends on how well it separates objects within a cluster from objects in other clusters. Hierarchical clustering creates clusters by iteratively merging or splitting groups of objects based on their distances in a dendrogram.
Cluster analysis is a technique used to classify objects into groups called clusters based on their similarities. It has many applications in areas like market research, biology, and image processing. There are different types of clustering methods like partitioning, hierarchical, density-based, and grid-based. The k-means algorithm is a commonly used partitioning method where objects are grouped into k clusters based on their distances from centroid points, which are recalculated in each iteration until cluster memberships stabilize. Cluster analysis helps discover patterns and insights from large datasets.
Cluster analysis is a technique used to group objects into clusters based on similarities. There are several major approaches to cluster analysis including partitioning methods, hierarchy methods, density-based methods, and grid-based methods. Partitioning methods construct partitions of the data objects into a set number of clusters by optimizing a chosen criterion, such as k-means and k-medoids clustering algorithms.
Building a Classifier Employing Prism Algorithm with Fuzzy LogicIJDKP
Classification in data mining is receiving immense interest in recent times. As the knowledge is based on
historical data, classifications of data are essential for discovering the knowledge. To decrease the
classification complexity, the quantitative attributes of data need splitting. But the splitting using the
classical logic is less accurate. This can be overcome by the use of fuzzy logic. This paper illustrates how to
build up the classification rules using the fuzzy logic. The fuzzy classifier is built on by using the prism
decision tree algorithm. This classifier produces more realistic results than the classical one. The
effectiveness of this method is justified over a sample dataset.
This document discusses cluster analysis and various clustering algorithms. It begins with an overview of supervised and unsupervised learning, as well as generative models. It then discusses 5 common clustering techniques: partitioning, hierarchical, density-based, grid-based, and model-based clustering. The document also covers challenges with cluster analysis such as centroid initialization, outlier handling, categorical data, the curse of dimensionality, and computational complexity. Specific clustering algorithms discussed in more detail include K-means, K-medoids, K-modes, mini-batch K-means, and scalable K-means++.
The document discusses different clustering techniques used for grouping large amounts of data. It covers partitioning methods like k-means and k-medoids that organize data into exclusive groups. It also describes hierarchical methods like agglomerative and divisive clustering that arrange data into nested groups or trees. Additionally, it mentions density-based and grid-based clustering and provides algorithms for different clustering approaches.
Cluster analysis is an unsupervised machine learning technique that groups unlabeled data points into clusters. The goal is to categorize data objects such that objects within a cluster are as similar as possible to each other, and as dissimilar as possible to objects in other clusters. Good clustering produces high quality clusters with high intra-class similarity and low inter-class similarity. Clustering has applications in marketing, land use analysis, insurance, and other domains.
Cluster analysis is an unsupervised learning technique that groups similar data objects into clusters. It finds internal structures within unlabeled data by grouping objects based on their characteristics. Clustering is used to gain insight into data distribution and as a preprocessing step for other algorithms. Some applications of clustering include marketing, land use analysis, insurance risk assessment, and city planning. The quality of clustering depends on how well it separates objects within a cluster from objects in other clusters. Hierarchical clustering creates clusters by iteratively merging or splitting groups of objects based on their distances in a dendrogram.
Cluster analysis is a technique used to classify objects into groups called clusters based on their similarities. It has many applications in areas like market research, biology, and image processing. There are different types of clustering methods like partitioning, hierarchical, density-based, and grid-based. The k-means algorithm is a commonly used partitioning method where objects are grouped into k clusters based on their distances from centroid points, which are recalculated in each iteration until cluster memberships stabilize. Cluster analysis helps discover patterns and insights from large datasets.
This document provides an overview of several clustering algorithms. It begins by defining clustering and its importance in data mining. It then categorizes clustering algorithms into four main types: partitional, hierarchical, grid-based, and density-based. For each type, some representative algorithms are described briefly. The document also reviews several popular clustering algorithms like k-means, CLARA, PAM, CLARANS, and BIRCH in more detail. It discusses aspects like the algorithms' time complexity, types of data handled, ability to detect clusters of different shapes, required input parameters, and advantages/disadvantages. Overall, the document aims to guide selection of suitable clustering algorithms for specific applications by surveying their key characteristics.
Introduction to Multi-Objective Clustering EnsembleIJSRD
Association rule mining is a popular and well researched method for discovering interesting relations between variables in large databases. In this paper we introduce the concept of Data mining, Association rule and Multilevel association rule with different algorithm, its advantage and concept of Fuzzy logic and Genetic Algorithm. Multilevel association rules can be mined efficiently using concept hierarchies under a support-confidence framework.
Data mining techniques are used to retrieve the knowledge from large databases that helps the
organizations to establish the business effectively in the competitive world. Sometimes, it violates privacy
issues of individual customers. In this paper we proposes An algorithm ,addresses the problem of privacy
issues related to the individual customers and also propose a transformation technique based on a Walsh-
Hadamard transformation (WHT) and Rotation. The WHT generates an orthogonal matrix, it transfers
entire data into new domain but maintain the distance between the data records these records can be
reconstructed by applying statistical based techniques i.e. inverse matrix, so this problem is resolved by
applying Rotation transformation. In this work, we increase the complexity to unauthorized persons for
accessing original data of other organizations by applying Rotation transformation. The experimental
results show that, the proposed transformation gives same classification accuracy like original data set. In
this paper we compare the results with existing techniques such as Data perturbation like Simple Additive
Noise (SAN) and Multiplicative Noise (MN), Discrete Cosine Transformation (DCT), Wavelet and First
and Second order sum and Inner product Preservation (FISIP) transformation techniques. Based on
privacy measures the paper concludes that proposed transformation technique is better to maintain the
privacy of individual customers.
An Iterative Improved k-means ClusteringIDES Editor
This document presents a new iterative improved k-means clustering algorithm.
The k-means clustering algorithm is widely used but depends on random initial starting points, which can impact the results. The new algorithm aims to provide better initial starting points to improve k-means clustering results.
The algorithm divides the data into K initial groups, calculates new cluster centers iteratively using a distance-based formula, assigns data points to clusters, and repeats until cluster centers no longer change. Experimental results on several datasets show the new algorithm converges in fewer iterations than standard k-means, demonstrating it finds better cluster solutions.
This is very simple introduction to Clustering with some real world example. At the end of lecture I use stackOverflow API to test some clustering. I also wants to try facebook but it has some problem with it's API
Classification on multi label dataset using rule mining techniqueeSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
It is a data mining technique used to place the data elements into their related groups. Clustering is the process of partitioning the data (or objects) into the same class, The data in one class is more similar to each other than to those in other cluster.
This document discusses different clustering methods in data mining. It begins by defining cluster analysis and its applications. It then categorizes major clustering methods into partitioning methods, hierarchical methods, density-based methods, grid-based methods, and model-based clustering methods. Finally, it provides details on partitioning methods like k-means and k-medoids clustering algorithms.
The document provides a literature review of different clustering techniques. It begins by defining clustering and its applications. It then categorizes and describes several clustering methods including hierarchical (BIRCH, CURE, CHAMELEON), partitioning (k-means, k-medoids), density-based (DBSCAN, OPTICS, DENCLUE), grid-based (CLIQUE, STING, MAFIA), and model-based (RBMN, SOM) methods. For each method, it discusses the algorithm, advantages, disadvantages and time complexity. The document aims to provide an overview of various clustering techniques for classification and comparison.
Data mining is utilized to manage huge measure of information which are put in the data ware houses and databases, to discover required information and data. Numerous data mining systems have been proposed, for example, association rules, decision trees, neural systems, clustering, and so on. It has turned into the purpose of consideration from numerous years. A re-known amongst the available data mining strategies is clustering of the dataset. It is the most effective data mining method. It groups the dataset in number of clusters based on certain guidelines that are predefined. It is dependable to discover the connection between the distinctive characteristics of data.
In k-mean clustering algorithm, the function is being selected on the basis of the relevancy of the function for predicting the data and also the Euclidian distance between the centroid of any cluster and the data objects outside the cluster is being computed for the clustering the data points. In this work, author enhanced the Euclidian distance formula to increase the cluster quality.
The problem of accuracy and redundancy of the dissimilar points in the clusters remains in the improved k-means for which new enhanced approach is been proposed which uses the similarity function for checking the similarity level of the point before including it to the cluster.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Survey on traditional and evolutionary clustering approacheseSAT Journals
Abstract Clustering deals with grouping up of similar objects. Unlike classification, clustering tries to group a set of objects and find whether there is some relationship between the objects whereas in classification a set of predefined classes will be known and it is enough to find which class a object belongs. Simply, classification is a supervised learning technique and clustering is an unsupervised learning technique. Clustering techniques apply when there is no class to be predicted but rather when the instances are to be divided into natural groups. These clusters presumably reflect some mechanism at work in the domain from which instances are drawn, a mechanism that causes some instances to bear a stronger resemblance to each other than they do to the remaining instances. It naturally requires different techniques to the classification and association learning methods .Clustering has many applications in various fields. In Software engineering it helps in reverse engineering, software maintenance and for re-building systems. It aims at breaking a larger problem into small pieces of understanding elements. There are many approaches available to carry out clustering. Since clustering has no particular methodology there are many methods available for carrying out clustering. There are many traditional as well as evolutionary methods available for carrying out clustering. In this paper various types of the above mentioned methods are described and some of them are compared. Each method has its own advantage and they can be used according to the needs of the user. Keywords: Clustering, Classification, Software Engineering, Traditional, Evolutionary.
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.
Clustering of high dimensionality data which can be seen in almost all fields these days is becoming
very tedious process. The key disadvantage of high dimensional data which we can pen down is curse
of dimensionality. As the magnitude of datasets grows the data points become sparse and density of
area becomes less making it difficult to cluster that data which further reduces the performance of
traditional algorithms used for clustering. Semi-supervised clustering algorithms aim to improve
clustering results using limited supervision. The supervision is generally given as pair wise
constraints; such constraints are natural for graphs, yet most semi-supervised clustering algorithms are
designed for data represented as vectors [2]. In this paper, we unify vector-based and graph-based
approaches. We first show that a recently-proposed objective function for semi-supervised clustering
based on Hidden Markov Random Fields, with squared Euclidean distance and a certain class of
constraint penalty functions, can be expressed as a special case of the global kernel k-means objective
[3]. A recent theoretical connection between global kernel k-means and several graph clustering
objectives enables us to perform semi-supervised clustering of data. In particular, some methods have
been proposed for semi supervised clustering based on pair wise similarity or dissimilarity
information. In this paper, we propose a kernel approach for semi supervised clustering and present in
detail two special cases of this kernel approach.
- 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.
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.
A survey on Efficient Enhanced K-Means Clustering Algorithmijsrd.com
Data mining is the process of using technology to identify patterns and prospects from large amount of information. In Data Mining, Clustering is an important research topic and wide range of unverified classification application. Clustering is technique which divides a data into meaningful groups. K-means clustering is a method of cluster analysis which aims to partition n observations into k clusters in which each observation belongs to the cluster with the nearest mean. In this paper, we present the comparison of different K-means clustering algorithms.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
This document summarizes an academic paper that proposes an innovative modified K-Mode clustering algorithm for categorical data. The paper begins by introducing clustering algorithms and discusses existing algorithms like K-Means, K-Medoids, and K-Mode that are used for numerical and categorical data. It then describes the limitations of traditional K-Mode clustering and proposes a modified K-Mode algorithm that aims to provide better initial cluster means/modes to result in clusters with better accuracy. The paper experimentally evaluates the traditional and modified K-Mode algorithms on large datasets to compare their performance for varying data values.
In the present day huge amount of data is generated in every minute and transferred frequently. Although
the data is sometimes static but most commonly it is dynamic and transactional. New data that is being
generated is getting constantly added to the old/existing data. To discover the knowledge from this
incremental data, one approach is to run the algorithm repeatedly for the modified data sets which is time
consuming. Again to analyze the datasets properly, construction of efficient classifier model is necessary.
The objective of developing such a classifier is to classify unlabeled dataset into appropriate classes. The
paper proposes a dimension reduction algorithm that can be applied in dynamic environment for
generation of reduced attribute set as dynamic reduct, and an optimization algorithm which uses the
reduct and build up the corresponding classification system. The method analyzes the new dataset, when it
becomes available, and modifies the reduct accordingly to fit the entire dataset and from the entire data
set, interesting optimal classification rule sets are generated. The concepts of discernibility relation,
attribute dependency and attribute significance of Rough Set Theory are integrated for the generation of
dynamic reduct set, and optimal classification rules are selected using PSO method, which not only
reduces the complexity but also helps to achieve higher accuracy of the decision system. The proposed
method has been applied on some benchmark dataset collected from the UCI repository and dynamic
reduct is computed, and from the reduct optimal classification rules are also generated. Experimental
result shows the efficiency of the proposed method.
This document provides an overview of unsupervised learning techniques. It begins with introductions to unsupervised learning and clustering as a machine learning task. It then describes different types of clustering techniques including partitioning methods like k-means and k-medoids, hierarchical clustering, and density-based methods. Applications of clustering like customer segmentation and anomaly detection are also discussed. Key aspects of clustering algorithms like determining the optimal number of clusters using the elbow method are explained through examples.
Clustering algorithms group similar objects together by identifying commonalities between data points. There are several types of clustering algorithms, including connectivity-based hierarchical clustering which connects objects into clusters based on distance; centroid-based clustering which represents clusters by central vectors like k-means; distribution-based clustering which models clusters as belonging to the same statistical distribution; and density-based clustering which identifies clusters as dense regions separated by sparse areas. Clustering has applications across many domains including biology, market research, medicine, social science, and computer science.
This document provides an overview of several clustering algorithms. It begins by defining clustering and its importance in data mining. It then categorizes clustering algorithms into four main types: partitional, hierarchical, grid-based, and density-based. For each type, some representative algorithms are described briefly. The document also reviews several popular clustering algorithms like k-means, CLARA, PAM, CLARANS, and BIRCH in more detail. It discusses aspects like the algorithms' time complexity, types of data handled, ability to detect clusters of different shapes, required input parameters, and advantages/disadvantages. Overall, the document aims to guide selection of suitable clustering algorithms for specific applications by surveying their key characteristics.
Introduction to Multi-Objective Clustering EnsembleIJSRD
Association rule mining is a popular and well researched method for discovering interesting relations between variables in large databases. In this paper we introduce the concept of Data mining, Association rule and Multilevel association rule with different algorithm, its advantage and concept of Fuzzy logic and Genetic Algorithm. Multilevel association rules can be mined efficiently using concept hierarchies under a support-confidence framework.
Data mining techniques are used to retrieve the knowledge from large databases that helps the
organizations to establish the business effectively in the competitive world. Sometimes, it violates privacy
issues of individual customers. In this paper we proposes An algorithm ,addresses the problem of privacy
issues related to the individual customers and also propose a transformation technique based on a Walsh-
Hadamard transformation (WHT) and Rotation. The WHT generates an orthogonal matrix, it transfers
entire data into new domain but maintain the distance between the data records these records can be
reconstructed by applying statistical based techniques i.e. inverse matrix, so this problem is resolved by
applying Rotation transformation. In this work, we increase the complexity to unauthorized persons for
accessing original data of other organizations by applying Rotation transformation. The experimental
results show that, the proposed transformation gives same classification accuracy like original data set. In
this paper we compare the results with existing techniques such as Data perturbation like Simple Additive
Noise (SAN) and Multiplicative Noise (MN), Discrete Cosine Transformation (DCT), Wavelet and First
and Second order sum and Inner product Preservation (FISIP) transformation techniques. Based on
privacy measures the paper concludes that proposed transformation technique is better to maintain the
privacy of individual customers.
An Iterative Improved k-means ClusteringIDES Editor
This document presents a new iterative improved k-means clustering algorithm.
The k-means clustering algorithm is widely used but depends on random initial starting points, which can impact the results. The new algorithm aims to provide better initial starting points to improve k-means clustering results.
The algorithm divides the data into K initial groups, calculates new cluster centers iteratively using a distance-based formula, assigns data points to clusters, and repeats until cluster centers no longer change. Experimental results on several datasets show the new algorithm converges in fewer iterations than standard k-means, demonstrating it finds better cluster solutions.
This is very simple introduction to Clustering with some real world example. At the end of lecture I use stackOverflow API to test some clustering. I also wants to try facebook but it has some problem with it's API
Classification on multi label dataset using rule mining techniqueeSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
It is a data mining technique used to place the data elements into their related groups. Clustering is the process of partitioning the data (or objects) into the same class, The data in one class is more similar to each other than to those in other cluster.
This document discusses different clustering methods in data mining. It begins by defining cluster analysis and its applications. It then categorizes major clustering methods into partitioning methods, hierarchical methods, density-based methods, grid-based methods, and model-based clustering methods. Finally, it provides details on partitioning methods like k-means and k-medoids clustering algorithms.
The document provides a literature review of different clustering techniques. It begins by defining clustering and its applications. It then categorizes and describes several clustering methods including hierarchical (BIRCH, CURE, CHAMELEON), partitioning (k-means, k-medoids), density-based (DBSCAN, OPTICS, DENCLUE), grid-based (CLIQUE, STING, MAFIA), and model-based (RBMN, SOM) methods. For each method, it discusses the algorithm, advantages, disadvantages and time complexity. The document aims to provide an overview of various clustering techniques for classification and comparison.
Data mining is utilized to manage huge measure of information which are put in the data ware houses and databases, to discover required information and data. Numerous data mining systems have been proposed, for example, association rules, decision trees, neural systems, clustering, and so on. It has turned into the purpose of consideration from numerous years. A re-known amongst the available data mining strategies is clustering of the dataset. It is the most effective data mining method. It groups the dataset in number of clusters based on certain guidelines that are predefined. It is dependable to discover the connection between the distinctive characteristics of data.
In k-mean clustering algorithm, the function is being selected on the basis of the relevancy of the function for predicting the data and also the Euclidian distance between the centroid of any cluster and the data objects outside the cluster is being computed for the clustering the data points. In this work, author enhanced the Euclidian distance formula to increase the cluster quality.
The problem of accuracy and redundancy of the dissimilar points in the clusters remains in the improved k-means for which new enhanced approach is been proposed which uses the similarity function for checking the similarity level of the point before including it to the cluster.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Survey on traditional and evolutionary clustering approacheseSAT Journals
Abstract Clustering deals with grouping up of similar objects. Unlike classification, clustering tries to group a set of objects and find whether there is some relationship between the objects whereas in classification a set of predefined classes will be known and it is enough to find which class a object belongs. Simply, classification is a supervised learning technique and clustering is an unsupervised learning technique. Clustering techniques apply when there is no class to be predicted but rather when the instances are to be divided into natural groups. These clusters presumably reflect some mechanism at work in the domain from which instances are drawn, a mechanism that causes some instances to bear a stronger resemblance to each other than they do to the remaining instances. It naturally requires different techniques to the classification and association learning methods .Clustering has many applications in various fields. In Software engineering it helps in reverse engineering, software maintenance and for re-building systems. It aims at breaking a larger problem into small pieces of understanding elements. There are many approaches available to carry out clustering. Since clustering has no particular methodology there are many methods available for carrying out clustering. There are many traditional as well as evolutionary methods available for carrying out clustering. In this paper various types of the above mentioned methods are described and some of them are compared. Each method has its own advantage and they can be used according to the needs of the user. Keywords: Clustering, Classification, Software Engineering, Traditional, Evolutionary.
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.
Clustering of high dimensionality data which can be seen in almost all fields these days is becoming
very tedious process. The key disadvantage of high dimensional data which we can pen down is curse
of dimensionality. As the magnitude of datasets grows the data points become sparse and density of
area becomes less making it difficult to cluster that data which further reduces the performance of
traditional algorithms used for clustering. Semi-supervised clustering algorithms aim to improve
clustering results using limited supervision. The supervision is generally given as pair wise
constraints; such constraints are natural for graphs, yet most semi-supervised clustering algorithms are
designed for data represented as vectors [2]. In this paper, we unify vector-based and graph-based
approaches. We first show that a recently-proposed objective function for semi-supervised clustering
based on Hidden Markov Random Fields, with squared Euclidean distance and a certain class of
constraint penalty functions, can be expressed as a special case of the global kernel k-means objective
[3]. A recent theoretical connection between global kernel k-means and several graph clustering
objectives enables us to perform semi-supervised clustering of data. In particular, some methods have
been proposed for semi supervised clustering based on pair wise similarity or dissimilarity
information. In this paper, we propose a kernel approach for semi supervised clustering and present in
detail two special cases of this kernel approach.
- 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.
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.
A survey on Efficient Enhanced K-Means Clustering Algorithmijsrd.com
Data mining is the process of using technology to identify patterns and prospects from large amount of information. In Data Mining, Clustering is an important research topic and wide range of unverified classification application. Clustering is technique which divides a data into meaningful groups. K-means clustering is a method of cluster analysis which aims to partition n observations into k clusters in which each observation belongs to the cluster with the nearest mean. In this paper, we present the comparison of different K-means clustering algorithms.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
This document summarizes an academic paper that proposes an innovative modified K-Mode clustering algorithm for categorical data. The paper begins by introducing clustering algorithms and discusses existing algorithms like K-Means, K-Medoids, and K-Mode that are used for numerical and categorical data. It then describes the limitations of traditional K-Mode clustering and proposes a modified K-Mode algorithm that aims to provide better initial cluster means/modes to result in clusters with better accuracy. The paper experimentally evaluates the traditional and modified K-Mode algorithms on large datasets to compare their performance for varying data values.
In the present day huge amount of data is generated in every minute and transferred frequently. Although
the data is sometimes static but most commonly it is dynamic and transactional. New data that is being
generated is getting constantly added to the old/existing data. To discover the knowledge from this
incremental data, one approach is to run the algorithm repeatedly for the modified data sets which is time
consuming. Again to analyze the datasets properly, construction of efficient classifier model is necessary.
The objective of developing such a classifier is to classify unlabeled dataset into appropriate classes. The
paper proposes a dimension reduction algorithm that can be applied in dynamic environment for
generation of reduced attribute set as dynamic reduct, and an optimization algorithm which uses the
reduct and build up the corresponding classification system. The method analyzes the new dataset, when it
becomes available, and modifies the reduct accordingly to fit the entire dataset and from the entire data
set, interesting optimal classification rule sets are generated. The concepts of discernibility relation,
attribute dependency and attribute significance of Rough Set Theory are integrated for the generation of
dynamic reduct set, and optimal classification rules are selected using PSO method, which not only
reduces the complexity but also helps to achieve higher accuracy of the decision system. The proposed
method has been applied on some benchmark dataset collected from the UCI repository and dynamic
reduct is computed, and from the reduct optimal classification rules are also generated. Experimental
result shows the efficiency of the proposed method.
This document provides an overview of unsupervised learning techniques. It begins with introductions to unsupervised learning and clustering as a machine learning task. It then describes different types of clustering techniques including partitioning methods like k-means and k-medoids, hierarchical clustering, and density-based methods. Applications of clustering like customer segmentation and anomaly detection are also discussed. Key aspects of clustering algorithms like determining the optimal number of clusters using the elbow method are explained through examples.
Clustering algorithms group similar objects together by identifying commonalities between data points. There are several types of clustering algorithms, including connectivity-based hierarchical clustering which connects objects into clusters based on distance; centroid-based clustering which represents clusters by central vectors like k-means; distribution-based clustering which models clusters as belonging to the same statistical distribution; and density-based clustering which identifies clusters as dense regions separated by sparse areas. Clustering has applications across many domains including biology, market research, medicine, social science, and computer science.
pratik meshram-Unit 5 (contemporary mkt r sch)Pratik Meshram
This document discusses various data analysis techniques including cluster analysis, multidimensional scaling, perceptual mapping, and discriminant analysis. It provides details on cluster analysis methods and processes. Cluster analysis involves grouping similar observations into clusters so that observations within a cluster are more similar to each other than observations in other clusters. The document discusses different clustering algorithms and applications. It also provides an example of using cluster analysis to segment customers of an auto insurance company based on preferences.
DATA
Data is any raw material or unorganized information.
CLUSTER
Cluster is group of objects that belongs to a same class.
Cluster is a set of tables physically stored together as one table that shares common columns.
http://phpexecutor.com
A Comparative Study Of Various Clustering Algorithms In Data MiningNatasha Grant
This document provides an overview and comparison of various clustering algorithms used in data mining. It discusses the key types of clustering algorithms: partition-based (such as k-means and k-medoids), hierarchical-based, density-based, and grid-based. For partition-based algorithms, it describes k-means and k-medoids in more detail. It also discusses hierarchical clustering approaches like agglomerative nesting. The document aims to provide insights into different clustering techniques for segmenting and grouping data in an unsupervised manner.
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UNIT-IV
Cluster Analysis: Types of Data in Cluster Analysis – A Categorization of Major Clustering Methods – Partitioning Methods – Hierarchical methods – Density, Based Methods – Grid, Based Methods – Model, Based Clustering Methods – Clustering High, Dimensional Data – Constraint, Based Cluster Analysis – Outlier Analysis.
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Cluster analysis is a technique used in data analysis and data mining to group similar data points or objects into clusters. The goal is to partition data into meaningful subgroups where data points within each cluster are more similar to each other than those in other clusters. There are various applications of cluster analysis across different fields like marketing, biology, image processing, and social sciences. Common cluster analysis methods include K-means clustering, hierarchical clustering, DBSCAN, and Gaussian mixture models. The choice of method depends on factors like the nature of data, number of desired clusters, and analysis objectives.
Clustering: Introduction, Types of clustering;
Partition-based clustering: K-Means, K-Medoids;
Density based clustering: DBSCAN, Clustering evaluation.
Mining Data Stream, Mining Time-Series Data, Mining Sequence Patterns in Transactional Database,
Social Network analysis and Multirelational Data Mining.
Multilevel techniques for the clustering problemcsandit
Data Mining is concerned with the discovery of interesting patterns and knowledge in data
repositories. Cluster Analysis which belongs to the core methods of data mining is the process
of discovering homogeneous groups called clusters. Given a data-set and some measure of
similarity between data objects, the goal in most clustering algorithms is maximizing both the
homogeneity within each cluster and the heterogeneity between different clusters. In this work,
two multilevel algorithms for the clustering problem are introduced. The multilevel
paradigm suggests looking at the clustering problem as a hierarchical optimization process
going through different levels evolving from a coarse grain to fine grain strategy. The clustering
problem is solved by first reducing the problem level by level to a coarser problem where an
initial clustering is computed. The clustering of the coarser problem is mapped back level-bylevel
to obtain a better clustering of the original problem by refining the intermediate different
clustering obtained at various levels. A benchmark using a number of data sets collected from a
variety of domains is used to compare the effectiveness of the hierarchical approach against its
single-level counterpart.
The document discusses knowledge discovery and data mining. It describes knowledge discovery as automatically searching large volumes of data for patterns that can be considered knowledge. The document outlines the five steps of the knowledge discovery process and notes it is closely related to data mining. It then discusses data mining, describing the purpose, preference, and search techniques used in data mining algorithms. The document also categorizes data mining and describes how it provides links between transactional and analytical systems to analyze relationships and patterns in stored data.
Applications Of Clustering Techniques In Data Mining A Comparative StudyFiona Phillips
This document discusses and compares various clustering techniques used in data mining. It begins with an introduction to data mining and clustering. It then discusses different types of clustering (hard vs soft), popular clustering methodologies like K-means, hierarchical, density-based etc. It provides examples of clustering applications. The document also discusses challenges in clustering large datasets and proposes approaches like MapReduce. It evaluates pros and cons of different clustering algorithms and their real-world applications.
Clustering is an unsupervised machine learning technique that groups unlabeled data points into clusters based on similarities. It partitions data into meaningful subgroups without predefined labels. Common clustering algorithms include k-means, hierarchical, density-based, and grid-based methods. K-means clustering aims to partition data into k clusters where each data point belongs to the cluster with the nearest mean. It is sensitive to outliers but simple and fast.
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.
Data Clustering Using Swarm Intelligence Algorithms An OverviewAboul Ella Hassanien
Bio-inspiring and evolutionary computation: Trends, applications and open issues workshop, 7 Nov. 2015 Faculty of Computers and Information, Cairo University
Data clustering and optimization techniquesSpyros Ktenas
This document discusses data clustering techniques and algorithms. It describes clustering as the process of separating a set of objects into logical groups based on similarity. Common clustering applications include classification of species, customer segmentation, and grouping search engine results. Popular clustering algorithms mentioned include k-means, hierarchical, distribution-based, and density-based clustering. The document also summarizes several papers that propose optimizations to clustering algorithms like k-means in order to improve accuracy and efficiency. Finally, it notes initial progress on a PHP implementation of the k-means algorithm.
A SURVEY ON OPTIMIZATION APPROACHES TO TEXT DOCUMENT CLUSTERINGijcsa
This document provides a survey of optimization approaches that have been applied to text document clustering. It discusses several clustering algorithms and categorizes them as partitioning methods, hierarchical methods, density-based methods, grid-based methods, model-based methods, frequent pattern-based clustering, and constraint-based clustering. It then describes several soft computing techniques that have been used as optimization approaches for text document clustering, including genetic algorithms, bees algorithms, particle swarm optimization, and ant colony optimization. These optimization techniques perform a global search to improve the quality and efficiency of document clustering algorithms.
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.
GraphSummit Singapore | The Future of Agility: Supercharging Digital Transfor...Neo4j
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In this work, we equipped AFL, a popular fuzzer, with DIAR and examined two critical Linux libraries -- Libxml's xmllint, a tool for parsing xml documents, and Binutil's readelf, an essential debugging and security analysis command-line tool used to display detailed information about ELF (Executable and Linkable Format). Our preliminary results show that AFL+DIAR does not only discover new paths more quickly but also achieves higher coverage overall. This work thus showcases how starting with lean and optimized seeds can lead to faster, more comprehensive fuzzing campaigns -- and DIAR helps you find such seeds.
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My slides at Nordic Testing Days 6.6.2024
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TrustArc Webinar - 2024 Global Privacy SurveyTrustArc
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Neha Bajwa, Vice President of Product Marketing, Neo4j
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In his public lecture, Christian Timmerer provides insights into the fascinating history of video streaming, starting from its humble beginnings before YouTube to the groundbreaking technologies that now dominate platforms like Netflix and ORF ON. Timmerer also presents provocative contributions of his own that have significantly influenced the industry. He concludes by looking at future challenges and invites the audience to join in a discussion.
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Observability Concepts EVERY Developer Should Know -- DeveloperWeek Europe.pdfPaige Cruz
Monitoring and observability aren’t traditionally found in software curriculums and many of us cobble this knowledge together from whatever vendor or ecosystem we were first introduced to and whatever is a part of your current company’s observability stack.
While the dev and ops silo continues to crumble….many organizations still relegate monitoring & observability as the purview of ops, infra and SRE teams. This is a mistake - achieving a highly observable system requires collaboration up and down the stack.
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Building Production Ready Search Pipelines with Spark and Milvus
ACO-medoids
1. University of Science and Technology Houari Boumediene
The ACO-MEDOIDS
Using the Ant Colony Optimization for partitioning
data into cluters
MOUDJARI Leila
l.moudj11@gmail.com
April 15, 2017
2. 1
Presentation plan
Introduction
Clustering and related work
What Is Cluster Analysis?
Requirements of clustering
Categorization of Clustering Methods
Clustering and related work
The importance of swarm intelligence and the ACO approach
Ant Colony Optimization
Adaptation of ACO to the medoids problem
ACO-MEDOID algorithm
An ant
The search space
Solution construction
Selecting rule
Fitness function
Pheromone update
The empirical parameters
Conclusion
MOUDJARI Leila | ACO-MEDOIDS
4. 2
Introduction
Data mining is used in several disciplines, database systems,
statistics, machine learning, visualization, information science...
MOUDJARI Leila | ACO-MEDOIDS
5. 2
Introduction
Data mining is used in several disciplines, database systems,
statistics, machine learning, visualization, information science...
A data mining system can perform several tasks such as
characterization, discrimination, association or correlation
analysis, classification, prediction, clustering, outlier analysis, or
evolution analysis. These tasks can be classified as supervised
or unsupervised. Data clustering is an unsupervised learning
and one of the most challenging problems in data mining. It’s
also classified as an NP-hard problem.
MOUDJARI Leila | ACO-MEDOIDS
6. 2
Introduction
Data mining is used in several disciplines, database systems,
statistics, machine learning, visualization, information science...
A data mining system can perform several tasks such as
characterization, discrimination, association or correlation
analysis, classification, prediction, clustering, outlier analysis, or
evolution analysis. These tasks can be classified as supervised
or unsupervised. Data clustering is an unsupervised learning
and one of the most challenging problems in data mining. It’s
also classified as an NP-hard problem.
One of the strongest disciplines which faced this class of
problems and still remains liable is swarm intelligence. Therefore
we leaned towards this discipline as other researchers did.
MOUDJARI Leila | ACO-MEDOIDS
8. 3
Introduction
Over the last years, many have presented works in this area, we
mention the BAT-CLARA [1], Association Rule Mining Based on
Bat Algorithm [2], MACOC: a medoid-based ACO clustering
algorithm [3], SACOC: A spectral-based ACO clustering
algorithm [4]...
MOUDJARI Leila | ACO-MEDOIDS
10. 4
Introduction
Clustering is a large field and lots of work might still be needed in
the different areas. However we are concetrating ours on the
partitioning algorithms. Pricesly partitioning the dataset into k
clusters. Which is also an NP-hard task.
MOUDJARI Leila | ACO-MEDOIDS
11. 4
Introduction
Clustering is a large field and lots of work might still be needed in
the different areas. However we are concetrating ours on the
partitioning algorithms. Pricesly partitioning the dataset into k
clusters. Which is also an NP-hard task.
The most well-known and commonly used partitioning methods
are k-means, k-medoids (PAM), and their variations [5].
Such as CLARA, CLARANS, CLAM (a recent one 2011, using a
hybrid metaheuristic between VNS and Tabu Search to solve the
problem of k-medoid clustering) [6], ...etc.
MOUDJARI Leila | ACO-MEDOIDS
12. 4
Introduction
Clustering is a large field and lots of work might still be needed in
the different areas. However we are concetrating ours on the
partitioning algorithms. Pricesly partitioning the dataset into k
clusters. Which is also an NP-hard task.
The most well-known and commonly used partitioning methods
are k-means, k-medoids (PAM), and their variations [5].
Such as CLARA, CLARANS, CLAM (a recent one 2011, using a
hybrid metaheuristic between VNS and Tabu Search to solve the
problem of k-medoid clustering) [6], ...etc.
We hereby present an algorithm for k-medoid clustering based
on an ACO solution search the ACO-medoids. As its name
indicates, the algorithm uses the Ant colony optimisation to
explore the search space looking for an optimal set of medoids
with reference to k-medoids for necessary clustering concepts.
MOUDJARI Leila | ACO-MEDOIDS
15. 5
Clustering and related work
What Is Cluster Analysis?
Clustering is an unsupervised learning process it does
not rely on predefined classes and class-labeled
training examples, therefore it is considered as a
form of learning by observation and not by examples.
MOUDJARI Leila | ACO-MEDOIDS
16. 5
Clustering and related work
What Is Cluster Analysis?
Clustering is an unsupervised learning process it does
not rely on predefined classes and class-labeled
training examples, therefore it is considered as a
form of learning by observation and not by examples.
It aims to reduce the data size by grouping similar
objects in one cluster, so Giving a set of data
objects a clustering algorithm must be capable of
grouping the different objects into classes, so that a
high intragroup similarity and a low inter-group
similarity are ensured.
MOUDJARI Leila | ACO-MEDOIDS
17. 5
Clustering and related work
What Is Cluster Analysis?
Clustering is an unsupervised learning process it does
not rely on predefined classes and class-labeled
training examples, therefore it is considered as a
form of learning by observation and not by examples.
It aims to reduce the data size by grouping similar
objects in one cluster, so Giving a set of data
objects a clustering algorithm must be capable of
grouping the different objects into classes, so that a
high intragroup similarity and a low inter-group
similarity are ensured.
The similarity or dissimilarity is assessed via a
distance measure(Euclidean or Manhattan distance
measures, or other distance measurements, may also be
used)
MOUDJARI Leila | ACO-MEDOIDS
19. 6
Clustering and related work
Requirements of clustering
Scalability,
MOUDJARI Leila | ACO-MEDOIDS
20. 6
Clustering and related work
Requirements of clustering
Scalability,
Ability to deal with different types of attributes,
MOUDJARI Leila | ACO-MEDOIDS
21. 6
Clustering and related work
Requirements of clustering
Scalability,
Ability to deal with different types of attributes,
Ability to deal with noisy data,
MOUDJARI Leila | ACO-MEDOIDS
22. 6
Clustering and related work
Requirements of clustering
Scalability,
Ability to deal with different types of attributes,
Ability to deal with noisy data,
High dimensionality (number of attributes)...
MOUDJARI Leila | ACO-MEDOIDS
23. 7
Categorization of Clustering Methods
In general, these algorithms can be classified into the following
categories:
MOUDJARI Leila | ACO-MEDOIDS
24. 7
Categorization of Clustering Methods
In general, these algorithms can be classified into the following
categories:
Partitioning methods
what characterizes this class is a predefined number k of partitions,
each partition represents a cluster. So that each cluster must contain
at least one object and an object must belong to at most one group.
The most known methods are k-means and k-medoids.
MOUDJARI Leila | ACO-MEDOIDS
25. 7
Categorization of Clustering Methods
In general, these algorithms can be classified into the following
categories:
Partitioning methods
what characterizes this class is a predefined number k of partitions,
each partition represents a cluster. So that each cluster must contain
at least one object and an object must belong to at most one group.
The most known methods are k-means and k-medoids.
Hierarchical methods
creates a hierarchical decomposition of the dataset, it can be
classified as being either agglomerative (bottom-up) or divisive
(top-down).
MOUDJARI Leila | ACO-MEDOIDS
26. 8
Categorization of Clustering Methods
Density-based methods
unlike partitioning methods, these are based on the notion of density
(number of objects or data points) instead of distance. They continue
growing the given cluster as long as the density in the “neighborhood”
exceeds some threshold. Such as DBSCAN and its extension,
OPTICS, are typical density-based methods.
MOUDJARI Leila | ACO-MEDOIDS
27. 8
Categorization of Clustering Methods
Density-based methods
unlike partitioning methods, these are based on the notion of density
(number of objects or data points) instead of distance. They continue
growing the given cluster as long as the density in the “neighborhood”
exceeds some threshold. Such as DBSCAN and its extension,
OPTICS, are typical density-based methods.
There is also the Grid-based methods, Model-based methods,
Constraint-based clustering...
MOUDJARI Leila | ACO-MEDOIDS
28. 9
Clustering and related work
K-mean algorithm
Input: k (the number of clusters),
D(a data set containing n objects).
Output: A set of k clusters.
Begin
1. arbitrarily choose k objects from D as the
initial cluster centers;
2. repeat
3. (re)assign each object to the cluster to
which the object is the most similar;
4. update the cluster means, i.e., calculate the
mean value of the objects for each cluster;
5. until no change;
End.
MOUDJARI Leila | ACO-MEDOIDS
29. 10
Clustering and related work
k-Medoids algorithm
Input: k (the number of clusters),
D(a data set containing n objects).
Output: A set of k clusters.
Begin
1. arbitrarily choose k objects from D as the initial cluster centers;
2. repeat
3. assign each remaining object to the nearest cluster;
4. randomly select a nonrepresentative object, orand ;
5. compute the total cost, S, of swapping
representative object, oj with orand ;
6. if S < 0 then swap oj with orand to form the new set of k
medoids;
7. until no change;
End.
MOUDJARI Leila | ACO-MEDOIDS
30. 11
Clustering and related work
K-medoids was presented as a solution to some of k-means flows. As
its sensitivity towards outliers and the fact that the centroids are
abstract objects. PAM proved that real objects diminish the error
value. However, it has some lacks. When it comes to large datasets it
loses due to the significant amount of time needed to construct the
set of medoids. In spite of that, researchers tried to improve it. That’s
why clustering field witnessed the birth of its variations: CLARA,
followed by CLARANS and others as already mentioned. However
the problem persists. How can we gain in scalability without
loosing in quality?
In the last years clustering draw attention of the meta-heuristic
community. Several works have been presented. One of the
promising optimization methods is ACO.
MOUDJARI Leila | ACO-MEDOIDS
31. 12
The importance of swarm intelligence and the
ACO approach
Swarm intelligence
MOUDJARI Leila | ACO-MEDOIDS
32. 12
The importance of swarm intelligence and the
ACO approach
Swarm intelligence
It is well known that we are more effective when we work with
others rather than working in isolation and this is, the core of
swarm intelligence.
MOUDJARI Leila | ACO-MEDOIDS
33. 12
The importance of swarm intelligence and the
ACO approach
Swarm intelligence
It is well known that we are more effective when we work with
others rather than working in isolation and this is, the core of
swarm intelligence.
Swarm intelligence is based on the collective behavior of
species. Each method is a result of nature observation and
intelligence forms of group behavior analysis. It results in the
simulation of these studied behaviors of collective insects, animal
and human. It gained popularity with the burst of artificial
intelligence in the 80s. Especially when dealing with
combinatorial problems. Such problems are divided into classes,
P (polynomial), NP, Np-complete and NP-hard. The latter two
generally have an exponential complexity.
MOUDJARI Leila | ACO-MEDOIDS
34. 13
The importance of swarm intelligence and the
ACO approach
Problem ∈ [Np-hard | Np-complete] ==> call 911.
clustering ∈ [Np-hard] ==> Swarm intelligence.
MOUDJARI Leila | ACO-MEDOIDS
35. 14
The importance of swarm intelligence and the
ACO approach
Ant Colony Optimization
ACO showed its strength when dealing with problems related to
graphs.
It was driven by the fascination for ants, how they worked in
harmony to nourish and build a habitat.
They cooperate and help each other by sharing useful
information such as the path to take or to avoid.
they communicate using a substance they release called
"pheromone", as a stigmergy.
The use of ACO-based algorithms is very large and domain
based, therefore it was adopted to several types of problems.
MOUDJARI Leila | ACO-MEDOIDS
36. 15
The importance of swarm intelligence and the
ACO approach
Ant Colony Optimization: the algorithm
ACO algorithm
Begin
1. While (not stop conditions) do
2. for k=1 to Nb-ants do
3. begin
4. Build a solution (Sk );
5. Evaluate (Sk );
6. Apply online pheromone update;
7. end-for;
8. Determine the best solution of the current iteration;
9. Apply offline pheromone update;
10. end-while;
End.
MOUDJARI Leila | ACO-MEDOIDS
37. 16
The importance of swarm intelligence and the
ACO approach
Ant Colony Optimization
One of the advantages of applying ACO algorithms to the
clustering problems is that ACO performs a global search in the
solution space, which is less likely to get trapped in local minima
and, thus, has the potential to find more accurate solutions [7].
The algorithm, uses an iterative search strategy to find an
approximate optimal solution, using the pheromone track and a
heuristic.
ACO has been successfully adopted for multiple problems.
Works on unsupervised learning have focused on clustering
showing the potential of ACO-based techniques.
MOUDJARI Leila | ACO-MEDOIDS
38. 17
Clustering and ACO
Nevertheless, more work need to be done, especially for
medoid-based clustering, which compared to classical
centroid-based techniques are more efficient. In this area, divers
algorithms were proposed such as:
"An adaptive multi-agent ACO clustering algorithm" in 2005 by
Weijiao Zhang and Chunhuang Liu.
"Classification with cluster-based Bayesian multi-nets using Ant
Colony Optimization" in 2014 by Khalid M. Selma and Alex A.
Freitas.
Also MACOC: a medoid-based ACO clustering algorithm in 2014.
Recently, a "Medoid-based clustering algorithms using ant
colony optimization" (METACOC and METACOC-K) were
proposed in 2016 (Héctor D. Menéndez, Fernando E. B. Otero,
David Camacho) [7].
...etc.
MOUDJARI Leila | ACO-MEDOIDS
39. 18
Adaptation of ACO to the medoids problem
ACO-MEDOID algorithm
MOUDJARI Leila | ACO-MEDOIDS
40. 18
Adaptation of ACO to the medoids problem
ACO-MEDOID algorithm
"ACO-medoids" for finding the best set of k-medoids. Based on the
ant colony optimisation and the k-medoids. we will strat with the
general form of the algorithm
MOUDJARI Leila | ACO-MEDOIDS
41. 18
Adaptation of ACO to the medoids problem
ACO-MEDOID algorithm
"ACO-medoids" for finding the best set of k-medoids. Based on the
ant colony optimisation and the k-medoids. we will strat with the
general form of the algorithm
ACO-medoid algorithm
Input: k (the number of clusters),
D(a data set containing n objects).
M(the similarity (distance) matrix).
Output: A set of k clusters.
Begin
// start by creating the initial population
1. foreach ant do
2. arbitrarily choose k objects from D as the initial solution of the ant;
3. end-foreach;
4. While (change or i < Max − Iter) do
5. foreach ant do
6. begin
7. Build a solution (Sk );
8. Evaluate (Sk );
9. Update Abest and Vbest 19;
10. Apply online pheromone update;
11. end-foreach;
12. Determine the best solution of the current iteration;
13. Apply offline pheromone update;
14. end-while;
End.
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42. 19
Adaptation of ACO to the medoids problem
An ant
A virtual agent in the multi-dimensional space, which is the search
space. It has the following properties:
sol: which is the current solution of the ant,
Abest: the best solution found so far by the ant,
Vbest: the valuation of Abest.
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43. 20
Adaptation of ACO to the medoids problem
The search space
It includes all potential combinations of objects that can build a set of
medoids (solutions), verifying the similarity/dissimilarity constraint of
clustering. The number of these possible solutions depends on k (the
number of clusters) so if we have n objects that need to be placed in
k clusters then the number is determined as follows:
For the initial object we have n possibilities,
for the next one we have n − 1,
for the kth
we have n − k − 1 possibilities,
The total number of solutions is then equal to
n ∗ (n − 1) ∗ ... ∗ (n − k − 1) => meaning exponential.
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44. 21
Adaptation of ACO to the medoids problem
Solution construction
In order to build a solution an ant has two possible strategies exploit
or explore. The first is a local search based method that helps an ant
improve its solution, the second help exploring new promising
regions. As shown in the next pseudocode;
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45. 21
Adaptation of ACO to the medoids problem
Solution construction
In order to build a solution an ant has two possible strategies exploit
or explore. The first is a local search based method that helps an ant
improve its solution, the second help exploring new promising
regions. As shown in the next pseudocode;
Procedure: constructSolution
Input: an ant,
Output: an ant
Begin
// choose a strategy randomly
1. S0 : a random variable uniformly distributed in [0,1]
2. if S0 <= Sp then
3. sol = explore;
4. applyLocalSearch(Sol);
5. else
6. apply local search(Abest);
7. endif;
End.
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Adaptation of ACO to the medoids problem
Solution construction
Procedure: explore
Input: D the dataset;
Output: s
Begin
1. s = empty;
2. while (i<k and D not empty) do
3. select oi from D using the selecting rule 24;
4. Append oi to s;
5. eliminate oi from D;
6. endwhile;
End.
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Adaptation of ACO to the medoids problem
Solution construction
Procedure: localSearch
Input: the solution to be improved ;
Output: a solution
Begin
1. for j = 1 to lmax do
2. for m=1 to mds 27 do
3. C: the corresponding cluster;
4. choose object orand from C;
5. compute the total cost S, of swapping the
representative object Sol[m], with orand ;
6. if S < 0 then swap orand with Sol[m] to
form the new set of k representative objects;
7. update clusters;
8. endfor;
9. endfor;
End.
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48. 24
Adaptation of ACO to the medoids problem
Selecting rule
The selecting process tries to find the furthest object in the selection
D from the set of objects already chosen as medoids, by using the
following formula;
j =
maxu∈Y {T(u)} if q ≤ q0
maxu∈Y {P(u)} otherwise
(1)
Pu(t) =
Tu(t)
v∈Y Tv
where;
Tj pheromone amount of the jth
object ∈ D,
Y set of possible medoids,
P the probability that data instance j could
be selected as a medoid
q is a random number distributed uniformly
in [0, 1],
q0 is an empirical parameter,
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49. 25
Adaptation of ACO to the medoids problem
Fitness function
It is used to evaluate a solution, it represents the cost (Ecost ) of a
solution. However, in order to compare two solutions we calculate S,
S = Snew − Sold . If S is negative, then the new solution is better than
the old one.
Ecost =
k
i=1
C
j=1
M[m, j]
where;
M is the distance matrix,
C is the number of objects in the clusteri .
Another possible objective function is the sum of the probability P
calculate in the following formula. The aim is to maximize it;
if q ≤ q0
P =
1 if j = argmaxu∈Y {T(u)}
0 otherwise
(2)
else P is calculated as formula 24.
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Adaptation of ACO to the medoids problem
Pheromone update
Regarding the pheromone updates we used the on and offline
updates calculated as follows;
Online update
Ti = (1 − ρ)Ti (t) + ρτ0
where;
ρ: is the evaporation rate and also an empirical parameter,
τ: is the initial value of pheromone. Offline update At the end of
each iteration, the offline update is performed. So the ant with the
best current solution deposits an amount of pheromone equal to
∆Ti (t). The update is performed using this formula:
Ti = (1 − ρ)Ti (t) + ρ∆Ti (t)
where;
∆Ti (t) =
1
C if the ant uses the object l
0 otherwise
(3)
C: the cost of the ant’s solution (Ecost 25).
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Adaptation of ACO to the medoids problem
The empirical parameters
This section presents the different empirical parameters that need to
be defined in order to improve the solution quality.
parameter role
A number of ants
Max-Iter Iterations number of the algorithm
lmax Iterations number of local search
Sp in [0,1] Intensification/diversification rate
the strategy rate
q0 selection rate
mds Number of clusters to be updated
(can be equal to k or randomly
chosen each time in [1-k])
ρ the evaporation rate
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52. 28
Conclusion
We presented some ideas for the use of ACO to solve the medoids
problem, through a proposed medoid and ACO based clustering
algorithm we called "ACO-medoids". It is based on the ants’ collective
behavior and k-medoids for building the clusters. Implementation and
tests need to be done so that we can be conclusive regarding the
algorithm behavior. However swarm based algorithms, including ACO
proved that they can improve the time/space complexity of NP-hard
problems. Therefore, we believe that the algorithm can provide the
optimal solution in a finite amount of time.
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54. 29
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Bat-clara: Bat-inspired algorithm for clustering large applications.
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Association rule mining based on bat algorithm.
Journal of Computational and Theoretical Nanoscience
12(7):1195-1200, 2015.
[3] Fernando E. B. Otero Héctor D. Menéndez and David Camacho.
Macoc: a medoid-based aco clustering algorithm.
DOI: 10.1007/978-3-319-09952-1_11, 2014.
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[6] V.J. J Nguyen, Q. & Rayward-Smith.MOUDJARI Leila | ACO-MEDOIDS