| Series |
River Publishers Series in Mathematical and Engineering Sciences Ser
River Publishers Series in Mathematical and Engineering Sciences Ser. UNAUTHORIZED
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| 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 |
| Contents |
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 |
| Contents |
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 |
| Contents |
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, ) -- 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, "", rr,T) -- 6.6.1 Choosing Termination and Iterate Limit Criteria -- 6.6.2 How to Pick an Initial V0 (or U0) |
| Contents |
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 |
| Contents |
7 Probabilistic Clustering -- GMD/EM |
| Abstract |
The availability of packaged clustering programs means that anyone with data can easily do cluster analysis on it. But many users of this technology don't fully appreciate its many hidden dangers. In today's world of "grab and go algorithms," part of my motivation for writing this book is to provide users with a set of cautionary tales about cluster analysis, for it is very much an art as well as a science, and it is easy to stumble if you don't understand its pitfalls. Indeed, it is easy to trip over them even if you do! The parenthetical word usually in the title is very important, because all clustering algorithms can and do fail from time to time. Modern cluster analysis has become so technically intricate that it is often hard for the beginner or the non-specialist to appreciate and understand its many hidden dangers. Here's how Yogi Berra put it, and he was right: In theory there's no difference between theory and practice. In practice, there is ~Yogi Berra This book is a step backwards, to four classical methods for clustering in small, static data sets that have all withstood the tests of time. The youngest of the four methods is now almost 50 years old: Gaussian Mixture Decomposition (GMD, 1898) SAHN Clustering (principally single linkage (SL, 1909)) Hard c-means (HCM, 1956, also widely known as (aka) "k-means") Fuzzy c-means (FCM, 1973, reduces to HCM in a certain limit) The dates are the first known writing (to me, anyway) about these four models. I am (with apologies to Marvel Comics) very comfortable in calling HCM, FCM, GMD and SL the Fantastic Four. Cluster analysis is a vast topic. The overall picture in clustering is quite overwhelming, so any attempt to swim at the deep end of the pool in even a very specialized subfield requires a lot of training. But we all start out at the shallow end (or at least that's where we should start!), and this book is aimed squarely at teaching toddlers not to be afraid of the water. There is no section of this book that, if explored in real depth, cannot be expanded into its own volume. So, if your needs are for an in-depth treatment of all the latest developments in any topic in this volume, the best I can do - what I will try to do anyway - is lead you to the pool, and show you where to jump in. |
| General note | Description based upon print version of record. |
| Biographical note | James C. Bezdek- Visiting Senior Fellow, University of Melbourne |
| Issued in other form | Print version: Bezdek, James C. Elementary Cluster Analysis: Four Basic Methods That (Usually) Work Aalborg : River Publishers,c2022 9788770224253 |
| ISBN | 9781000794786 |
| ISBN | 1000794784 |
| ISBN | 9781003338086 (electronic bk.) |
| ISBN | 1003338089 (electronic bk.) |
| ISBN | 9781000791662 (electronic bk. : EPUB) |
| ISBN | 1000791661 (electronic bk. : EPUB) |
| ISBN | 9788770224246 |
| ISBN | 8770224242 |
| Standard identifier# |
10.1201/9781003338086 |
| Stock number | 9781003338086 Taylor & Francis |
