Metaheuristic Clustering (Studies in Computational Intelligence (178))

Cluster analysis means the organization of an unlabeled collection of objects or patterns into separate groups based on their similarity. The task of computerized data clustering has been approached from diverse domains of knowledge like graph theory, multivariate analysis, neural networks, fuzzy set theory, and so on. Clustering is often described as an unsupervised learning method but most of the traditional algorithms require a prior specification of the number of clusters in the data for guiding the partitioning process, thus making it not completely unsupervised. Modern data mining tools that predict future trends and behaviors for allowing businesses to make proactive and knowledge-driven decisions, demand fast and fully automatic clustering of very large datasets with minimal or no user intervention. In this Volume, we formulate clustering as an optimization problem, where the best partitioning of a given dataset is achieved by minimizing/maximizing one (single-objective clustering) or more (multi-objective clustering) objective functions. Using several real world applications, we illustrate the performance of several metaheuristics, particularly the Differential Evolution algorithm when applied to both single and multi-objective clustering problems, where the number of clusters is not known beforehand and must be determined on the run. This volume comprises of 7 chapters including an introductory chapter giving the fundamental definitions and the last Chapter provides some important research challenges. Academics, scientists as well as engineers engaged in research, development and application of optimization techniques and data mining will find the comprehensive coverage of this book invaluable. Metaheuristic Pattern Clustering – An Overview 18 Introduction 18 The Clustering Problem 18 $Basic Definitions$ 18 $Proximity Measures$ 18 $Clustering Validity Indices$ 18 The Classical Clustering Algorithms 18 $Hierarchical Clustering Algorithms$ 18 $Partitional Clustering Algorithms$ 18 $Density-Based Clustering Algorithms$ 18 $Grid-Based Clustering Algorithms$ 18 $A Comparative View of the Traditional Clustering Algorithms$ 18 Population Based Optimization Techniques 18 $Optimization Algorithms$ 18 $The Evolutionary Computing (EC) Family$ 18 $The Evolutionary Algorithms$ 18 $Swarm Intelligence Algorithms$ 18 $Evolutionary Computing (EC) Techniques in Pattern Clustering$ 18 Clustering Methods Based on Evolutionary Algorithms 18 $The GA-Based Partitional Clustering Algorithms - Earlier Approaches$ 18 $Clustering Algorithms Based on ES, EP, and GP$ 18 Clustering Using Swarm Intelligence Algorithms 18 $The Ant Colony Based Clustering Algorithms$ 18 $The PSO-Based Clustering Algorithms$ 18 Automatic Clustering: Evolutionary Vs. Classical Approaches 18 $Genetic Clustering with Unknown Number of Clusters K (GCUK) Algorithm$ 18 $The FVGA Algorithm$ 18 $The Dynamic Clustering with Particle Swarm Optimization Algorithm$ 18 Clustering with Evolutionary Multi-objective Optimization 18 $Multi-objective Optimization Problem (MOP)$ 18 $Evolutionary Multi-objective Optimization (EMO)$ 18 $Clustering Using EMO Algorithms (EMOAs)$ 18 Innovation and Research: Main Contributions of This Volume 18 Conclusions 18 References 18 Differential Evolution Algorithm: Foundations and Perspectives 80 Introduction 80 Differential Evolution: A First Glance 80 $Initialization of the Parameter Vectors$ 80 $Mutation with Differential Operators$ 80 $Crossover$ 80 $Selection$ 80 $Summary of DE Iteration$ 80 The Complete Differential Evolution Algorithm Family of Storn and Price 80 Control Parameters of the Differential Evolution 80 Important Variants of the Differential Evolution Algorithm 80 $Differential Evolution Using Trigonometric Mutation$ 80 $Differential Evolution Using Arithmetic Recombination$ 80 $Self Adaptive Differential Evolution$ 80 $The DE/rand/1/Either-Or Algorithm$ 80 $The Opposition-Based Differential Evolution$ 80 $The Binary Differential Evolution Algorithm$ 80 $Differential Evolution with Adaptive Local Search$ 80 $Self-adaptive Differential Evolution (SaDE) with Strategy Adaptation$ 80 $DE with Neighborhood-Based Mutation$ 80 Hybridization of Differential Evolution with Other Stochastic Search Techniques 80 Conclusions 80 References 80 Modeling and Analysis of the Population-Dynamics of Differential Evolution Algorithm 128 Introduction 128 The Mathematical Model of the Population-Dynamics in DE 128 $Assumptions$ 128 $Modeling Different Steps of DE$ 128 A State Space Formulation of the DE Population 128 Lyapunov Stability Analysis of the DE Population 128 Computer Simulation Results 128 Conclusions 128 Appendix 128 References 128 Automatic Hard Clustering Using Improved Differential Evolution Algorithm 153 Introduction 153 The DE-Based Automatic Clustering Algorithm 153 $Vector Representation$ 153 $Designing the Fitness Function$ 153 $Avoiding Erroneous Vectors$ 153 $Modification of the Classical DE$ 153 $Pseudo-code of the ACDE Algorithm$ 153 Experiments and Results for Real Life Datasets 153 $The Datasets Used$ 153 $Population Initialization$ 153 $Parameter Setup for the Algorithms Compared$ 153 $Simulation Strategy$ 153 $Empirical Results$ 153 $Discussion on the Results (for Real Life Datasets)$ 153 Application to Image Segmentation 153 $Image Segmentation as a Clustering Problem$ 153 $Experimental Details and Results$ 153 $Discussion on Image Segmentation Results$ 153 Conclusions 153 Appendix: Statistical Tests Used 153 References 153 Fuzzy Clustering in the Kernel-Induced Feature Space Using Differential Evolution Algorithm 191 Introduction 191 The Kernel-Induced Clustering 191 The Kernel-Induced Clustering Technique with DEGL 191 $Kernelization of the Xie-Beni Index$ 191 $Summary of the Integrated Clustering Approach$ 191 Experimental Results 191 $General Comparison with Other Clustering Algorithms$ 191 $Scalability of the DEGL-Based Clustering Algorithm$ 191 Application to Image Pixel Clustering 191 $Parametric Setup for the Contestant Algorithms$ 191 $The Test-Suite for Comparison$ 191 $Quantitative Validation of Clustering Results$ 191 $The Simulation Strategy$ 191 $Experimental Results$ 191 $Discussion on the Results$ 191 Conclusions 191 References 191 Clustering Using Multi-objective Differential Evolution Algorithms 228 Introduction 228 Multi-objective Optimization Using Differential Evolution Algorithm 228 $The Pareto Differential Evolution (PDE)$ 228 $The Multi-Objective Differential Evolution (MODE)$ 228 $Differential Evolution for Multi-objective Optimization (DEMO)$ 228 $Non-dominated Sorting DE (NSDE)$ 228 The Multi-objective Clustering Scheme 228 $Search-Variable Representation$ 228 $Selecting the Objective Functions$ 228 $Selecting the Best Solutions from Pareto-front$ 228 $Evaluating the Clustering Quality$ 228 Experiments and Results 228 $Datasets Used$ 228 $Parameters for the Algorithms$ 228 $Presentation of Results$ 228 $Significance and Validation of Microarray Data Clustering Results$ 228 Conclusions 228 References 228 Conclusions and Future Research 254 Cluster Analysis Using Metaheuristics: A Roadmap of This Volume 254 Potential Application Areas for Clustering Schemes 254 Future Research Directions 254 References 254 The year 2008 is a memorial year for Georgiy Voronoi (1868 -1908), with a number of events in the scientific community commemorating his tremendous contribution to the area of mathematics, especially number theory, through conferences and scientific gatherings in his honor. A notable event taking place in September 2008 a joint conference: the 5th Annual International Symposium on Voronoi Diagrams (ISVD) and the 4th International Conference on Analytic Number Theory and Spatial Tessellations held in Kyiv, Georgiy Voronoi's native land. The main ideas expressed by G. Voronoi's through his fundamental works have influenced and shaped the key developments in computation geometry, image recognition, artificial intelligence, robotics, computational science, navigation and obstacle avoidance, geographical information systems, molecular modeling, astrology, physics, quantum computing, chemical engineering, material sciences, terrain modeling, biometrics and other domains. This book is intended to provide the reader with in-depth overview and analysis of the fundamental methods and techniques developed following G. Voronoi ideas, in the context of the vast and increasingly growing area of computational intelligence. It represents the collection of state-of-the art research methods merging the bridges between two areas: geometric computing through Voronoi diagrams and intelligent computation techniques, pushing the limits of current knowledge in the area, improving on previous solutions, merging sciences together, and inventing new ways of approaching difficult applied problems. Some chapters of the book were invited following the successful 3rd Annual International Symposium on Voronoi Diagrams (ISVD'06), that took place in Banff, Canada, in June 2006. Some others are direct submissions by leading international experts in the prospective areas

Cluster analysis means the organization of an unlabeled collection of objects or patterns into separate groups based on their similarity. The task of computerized data clustering has been approached from diverse domains of knowledge like graph theory, multivariate analysis, neural networks, fuzzy set theory, and so on. Clustering is often described as an unsupervised learning method but most of the traditional algorithms require a prior specification of the number of clusters in the data for guiding the partitioning process, thus making it not completely unsupervised. Modern data mining tools that predict future trends and behaviors for allowing businesses to make proactive and knowledge-driven decisions, demand fast and fully automatic clustering of very large datasets with minimal or no user intervention.

In this volume, we formulate clustering as an optimization problem, where the best partitioning of a given dataset is achieved by minimizing/maximizing one (single-objective clustering) or more (multi-objective clustering) objective functions. Using several real world applications, we illustrate the performance of several metaheuristics, particularly the Differential Evolution algorithm when applied to both single and multi-objective clustering problems, where the number of clusters is not known beforehand and must be determined on the run. This volume comprises of 7 chapters including an introductory chapter giving the fundamental definitions and the last Chapter provides some important research challenges.

Academics, scientists as well as engineers engaged in research, development and application of optimization techniques and data mining will find the comprehensive coverage of this book invaluable.

The year 2008 is a memorial year for Georgiy Vorono (1868-1908), with a number of events in the scientific community commemorating his tremendous contribution to the area of mathematics, especially number theory, through conferences and scientific gatherings in his honor. A notable event taking place in September 2008 a joint c- ference: the 5th Annual International Symposium on Voronoi Diagrams (ISVD) and the 4th International Conference on Analytic Number Theory and Spatial Tessel- tions held in Kyiv, Georgiy Vorono's native land. The main ideas expressed by G. Vorono's through his fundamental works have influenced and shaped the key dev- opments in computation geometry, image recognition, artificial intelligence, robotics, computational science, navigation and obstacle avoidance, geographical information systems, molecular modeling, astrology, physics, quantum computing, chemical en- neering, material sciences, terrain modeling, biometrics and other domains. This book is intended to provide the reader with in-depth overview and analysis of the fundamental methods and techniques developed following G. Voronoi ideas, in the context of the vast and increasingly growing area of computational intelligence. It represents the collection of state-of-the art research methods merging the bridges between two areas: geometric computing through Voronoi diagrams and intelligent computation techniques, pushing the limits of current knowledge in the area, impr- ing on previous solutions, merging sciences together, and inventing new ways of approaching difficult applied problems. The purpose of this volume is to present current work of the Intelligent Computer Graphics community, a community growing up year after year. Indeed, if at the beg- ning of Computer Graphics the use of Artificial Intelligence techniques was quite unknown, more and more researchers all over the world are nowadays interested in intelligent techniques allowing substantial improvements of traditional Computer Graphics methods. The other main contribution of intelligent techniques in Computer Graphics is to allow invention of completely new methods, often based on automation of a lot of tasks assumed in the past by the user in an imprecise and (human) time consuming manner. The history of research in Computer Graphics is very edifying. At the beginning, due to the slowness of computers in the years 1960, the unique research concern was visualisation. The purpose of Computer Graphics researchers was to find new visua- sation algorithms, less and less time consuming, in order to reduce the enormous time required for visualisation. A lot of interesting algorithms were invented during these first years of research in Computer Graphics. The scenes to be displayed were very simple because the computing power of computers was very low. So, scene modelling was not necessary and scenes were designed directly by the user, who had to give co-ordinates of vertices of scene polygons. In recent years, the issue of linkage in GEAs has garnered greater attention and recognition from researchers. Conventional approaches that rely much on ad hoc tweaking of parameters to control the search by balancing the level of exploitation and exploration are grossly inadequate. As shown in the work reported here, such parameters tweaking based approaches have their limits; they can be easily "fooled" by cases of triviality or peculiarity of the class of problems that the algorithms are designed to handle. Furthermore, these approaches are usually blind to the interactions between the decision variables, thereby disrupting the partial solutions that are being built up along the way. The whole volume consisting of 19 chapters is divided into 3 parts: Models and Theories; Operators and Frameworks; Applications. This edited volume will serve as a useful guide and reference for researchers who are currently working in the area of linkage. For postgraduate research students, this volume will serve as a good source of reference. It is also suitable as a text for a graduate level course focusing on linkage issues. For practitioners who are looking at putting into practice the concept of linkage, the few chapters on applications will serve as a useful guide

the Purpose Of This Volume Is To Present Current Work Of The Intelligent Computer Graphics Community, A Community Growing Up Year After Year. Indeed, If At The Beginning Of Computer Graphics The Use Of Artificial Intelligence Techniques Was Quite Unknown, More And More Researchers All Over The World Are Nowadays Interested In Intelligent Techniques Allowing Substantial Improvements Of Traditional Computer Graphics Methods. The Other Main Contribution Of Intelligent Techniques In Computer Graphics Is To Allow Invention Of Completely New Methods, Often Based On Automation Of A Lot Of Tasks Assumed In The Past By The User In An Imprecise And (human) Time Consuming Manner.

this Volume Contains Both Invited And Selected Extended Papers From The Last 3ia Conference (3ia’2008), Together With An Introduction Presenting The Area Of Intelligent Computer Graphics And Various Computer Graphics Areas Where Introduction Of Intelligent Techniques Permitted To Resolve Important Problems. We Hope That This Volume Will Be Interesting For The Reader And That It Will Convince Him (her) To Use, Or To Invent, Intelligent Techniques In Computer Graphics And, Maybe, To Join The Intelligent Computer Graphics Community.

The purpose of this volume is to present current work of the Intelligent Computer Graphics community, a community growing up year after year. Indeed, if at the beginning of Computer Graphics the use of Artificial Intelligence techniques was quite unknown, more and more researchers all over the world are nowadays interested in intelligent techniques allowing substantial improvements of traditional Computer Graphics methods. The other main contribution of intelligent techniques in Computer Graphics is to allow invention of completely new methods, often based on automation of a lot of tasks assumed in the past by the user in an imprecise and (human) time consuming manner. This volume contains both invited and selected extended papers from the last 3IA Conference (3IA'2008), together with an introduction presenting the area of Intelligent Computer Graphics and various Computer Graphics areas where introduction of intelligent techniques permitted to resolve important problems. We hope that this volume will be interesting for the reader and that it will convince him (her) to use, or to invent, intelligent techniques in Computer Graphics and, maybe, to join the Intelligent Computer Graphics community. Front Matter....Pages - Metaheuristic Pattern Clustering – An Overview....Pages 1-62 Differential Evolution Algorithm: Foundations and Perspectives....Pages 63-110 Modeling and Analysis of the Population-Dynamics of Differential Evolution Algorithm....Pages 111-135 Automatic Hard Clustering Using Improved Differential Evolution Algorithm....Pages 137-174 Fuzzy Clustering in the Kernel-Induced Feature Space Using Differential Evolution Algorithm....Pages 175-211 Clustering Using Multi-objective Differential Evolution Algorithms....Pages 213-238 Conclusions and Future Research....Pages 239-247 Back Matter....Pages - Bayesian networks currently provide one of the most rapidly growing areas of research in computer science and statistics. In compiling this volume we have brought together contributions from some of the most prestigious researchers in this field. Each of the twelve chapters is self-contained. Both theoreticians and application scientists/engineers in the broad area of artificial intelligence will find this volume valuable. It also provides a useful sourcebook for Graduate students since it shows the direction of current research. Bayesian networks currently provide one of the most rapidly growing areas of research in computer science and statistics. In compiling this volume the editors have brought together contributions from some of the most prestigious researchers in this field