Elementary Cluster Analysis : : Four Basic Methods That (Usually) Work.

• Author: Bezdek, James C.
• Place / Publishing House: Denmark : : River Publishers,, 2022.; Ã2022.
• Year of Publication: 2022
• Edition: 1st ed.
• Language: English
• Physical Description: 1 online resource (518 pages)

Table of Contents

• Front Cover
• Elementary Cluster Analysis: Four Basic Methods that (Usually) Work
• Contents
• Preface
• List of Figures
• List of Tables
• List of Abbreviations
• Appendix A. List of Algorithms
• Appendix D. List of Definitions
• Appendix E. List of Examples
• Appendix L. List of Lemmas and Theorems
• Appendix V. List of Video Links
• I The Art and Science of Clustering
• 1 Clusters: The Human Point of View (HPOV)
• 1.1 Introduction
• 1.2 What are Clusters?
• 1.3 Notes and Remarks
• 1.4 Exercises
• 2 Uncertainty: Fuzzy Sets and Models
• 2.1 Introduction
• 2.2 Fuzzy Sets and Models
• 2.3 Fuzziness and Probability
• 2.4 Notes and Remarks
• 2.5 Exercises
• 3 Clusters: The Computer Point of View (CPOV)
• 3.1 Introduction
• 3.2 Label Vectors
• 3.3 Partition Matrices
• 3.4 How Many Clusters are Present in a Data Set?
• 3.5 CPOV Clusters: The Computer's Point of View
• 3.6 Notes and Remarks
• 3.7 Exercises
• 4 The Three Canonical Problems
• 4.1 Introduction
• 4.2 Tendency Assessment - (Are There Clusters?)
• 4.2.1 An Overview of Tendency Assessment
• 4.2.2 Minimal Spanning Trees (MSTs)
• 4.2.3 Visual Assessment of Clustering Tendency
• 4.2.4 The VAT and iVAT Reordering Algorithms
• 4.3 Clustering (Partitioning the Data into Clusters)
• 4.4 Cluster Validity (Which Clusters are "Best"?)
• 4.5 Notes and Remarks
• 4.6 Exercises
• 5 Feature Analysis
• 5.1 Introduction
• 5.2 Feature Nomination
• 5.3 Feature Analysis
• 5.4 Feature Selection
• 5.5 Feature Extraction
• 5.5.1 Principal Components Analysis
• 5.5.2 Random Projection
• 5.5.3 Sammon's Algorithm
• 5.5.4 Autoencoders
• 5.5.5 Relational Data
• 5.6 Normalization and Statistical Standardization
• 5.7 Notes and Remarks
• 5.8 Exercises
• II Four Basic Models and Algorithms
• 6 The c-Means (aka k-Means) Models
• 6.1 Introduction.
• 6.2 The Geometry of Partition Spaces
• 6.3 The HCM/FCM Models and Basic AO Algorithms
• 6.4 Cluster Accuracy for Labeled Data
• 6.5 Choosing Model Parameters (c, m, ||*||A)
• 6.5.1 How to Pick the Number of Clusters c
• 6.5.2 How to Pick the Weighting Exponent m
• 6.5.3 Choosing the Weight Matrix (A) for the Model Norm
• 6.6 Choosing Execution Parameters (V0, ", ||*||err,T)
• 6.6.1 Choosing Termination and Iterate Limit Criteria
• 6.6.2 How to Pick an Initial V0 (or U0)
• 6.6.3 Acceleration Schemes for HCM (aka k-Means) and (FCM)
• 6.7 Cluster Validity With the Best c Method
• 6.7.1 Scale Normalization
• 6.7.2 Statistical Standardization
• 6.7.3 Stochastic Correction for Chance
• 6.7.4 Best c Validation With Internal CVIs
• 6.7.5 Crisp Cluster Validity Indices
• 6.7.6 Soft Cluster Validity Indices
• 6.8 Alternate Forms of Hard c-Means (aka k-Means)
• 6.8.1 Bounds on k-Means in Randomly Projected Downspaces
• 6.8.2 Matrix Factorization for HCM for Clustering
• 6.8.3 SVD: A Global Bound for J1 (U, V
• X)
• 6.9 Notes and Remarks
• 6.10 Exercises
• 7 Probabilistic Clustering - GMD/EM
• 7.1 Introduction
• 7.2 The Mixture Model
• 7.3 The Multivariate Normal Distribution
• 7.4 Gaussian Mixture Decomposition
• 7.5 The Basic EM Algorithm for GMD
• 7.6 Choosing Model and Execution Parameters for EM
• 7.6.1 Estimating c With iVAT
• 7.6.2 Choosing Q0 or P0 in GMD
• 7.6.3 Implementation Parameters ", ||*||err,T for GMD With EM
• 7.6.4 Acceleration Schemes for GMD With EM
• 7.7 Model Selection and Cluster Validity for GMD
• 7.7.1 Two Interpretations of the Objective of GMD
• 7.7.2 Choosing the Number of Components Using GMD/EM With GOFIs
• 7.7.3 Choosing the Number of Clusters Using GMD/EM With CVIs
• 7.8 Notes and Remarks
• 7.9 Exercises
• 8 Relational Clustering - The SAHN Models
• 8.1 Relations and Similarity Measures.
• 8.2 The SAHN Model and Algorithms
• 8.3 Choosing Model Parameters for SAHN Clustering
• 8.4 Dendrogram Representation of SAHN Clusters
• 8.5 SL Implemented With Minimal Spanning Trees
• 8.5.1 The Role of the MST in Single Linkage Clustering
• 8.5.2 SL Compared to a Fitch-Margoliash Dendrogram
• 8.5.3 Repairing SL Sensitivity to Inliers and Bridge Points
• 8.5.4 Acceleration of the Single Linkage Algorithm
• 8.6 Cluster Validity for Single Linkage
• 8.7 An Example Using All Four Basic Models
• 8.8 Notes and Remarks
• 8.9 Exercises
• 9 Properties of the Fantastic Four: External Cluster Validity
• 9.1 Introduction
• 9.2 Computational Complexity
• 9.2.1 Using Big-Oh to Measure the Growth of Functions
• 9.2.2 Time and Space Complexity for the Fantastic Four
• 9.3 Customizing the c-Means Models to Account for Cluster Shape
• 9.3.1 Variable Norm Methods
• 9.3.2 Variable Prototype Methods
• 9.4 Traversing the Partition Landscape
• 9.5 External Cluster Validity With Labeled Data
• 9.5.1 External Paired-Comparison Cluster Validity Indices
• 9.5.2 External Best Match (Best U, or Best E) Validation
• 9.5.3 The Fantastic Four Use Best E Evaluations on Labeled Data
• 9.6 Choosing an Internal CVI Using Internal/External (Best I/E) Correlation
• 9.7 Notes and Remarks
• 9.8 Problems
• 10 Alternating Optimization
• 10.1 Introduction
• 10.2 General Considerations on Numerical Optimization
• 10.2.1 Iterative Solution of Optimization Problems
• 10.2.2 Iterative Solution of Alternating Optimization with (t, s) Schemes
• 10.3 Local Convergence Theory for AO
• 10.4 Global Convergence Theory
• 10.5 Impact of the Theory for the c-Means Models
• 10.6 Convergence for GMD Using EM/AO
• 10.7 Notes and Remarks
• 10.8 Exercises
• 11 Clustering in Static Big Data
• 11.1 The Jungle of Big Data
• 11.1.1 An Overview of Big Data.
• 11.1.2 Scalability vs. Acceleration
• 11.2 Methods for Clustering in Big Data
• 11.3 Sampling Functions
• 11.3.1 Chunk Sampling
• 11.3.2 Random Sampling
• 11.3.3 Progressive Sampling
• 11.3.4 Maximin (MM) Sampling
• 11.3.5 Aggregation and Non-Iterative Extension of a Literal Partition to the Rest of the Data
• 11.4 A Sampler of Other Methods: Precursors to Streaming Data Analysis
• 11.5 Visualization of Big Static Data
• 11.6 Extending Single Linkage for Static Big Data
• 11.7 Notes and Remarks
• 11.8 Exercises
• 12 Structural Assessment in Streaming Data
• 12.1 Streaming Data Analysis
• 12.1.1 The Streaming Process
• 12.1.2 Computational Footprints
• 12.2 Streaming Clustering Algorithms
• 12.2.1 Sequential Hard c-Means and Sebestyen's Method
• 12.2.2 Extensions of Sequential Hard c-Means: BIRCH, CluStream, and DenStream
• 12.2.3 Model-Based Algorithms
• 12.2.4 Projection and Grid-Based Methods
• 12.3 Reading the Footprints: Hindsight Evaluation
• 12.3.1 When You Can See the Data and Footprints
• 12.3.2 When You Can't See the Data and Footprints
• 12.3.3 Change Point Detection
• 12.4 Dynamic Evaluation of Streaming Data Analysis
• 12.4.1 Incremental Stream Monitoring Functions (ISMFs)
• 12.4.2 Visualization of Streaming Data
• 12.5 What's Next for Streaming Data Analysis?
• 12.6 Notes and Remarks
• 12.7 Exercises
• References
• Index
• About the Author
• Back Cover.