Co Clustering Models algorithms and applications 1st Edition by Gérard Govaert, Mohamed Nadif ISBN 1848214736 978-1848214736

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ISBN 10:  1848214736 

ISBN 13: 978-1848214736

Author: Gérard Govaert, Mohamed Nadif

Cluster or co-cluster analyses are important tools in a variety of scientific areas. The introduction of this book presents a state of the art of already well-established, as well as more recent methods of co-clustering. The authors mainly deal with the two-mode partitioning under different approaches, but pay particular attention to a probabilistic approach.

Chapter 1 concerns clustering in general and the model-based clustering in particular. The authors briefly review the classical clustering methods and focus on the mixture model. They present and discuss the use of different mixtures adapted to different types of data. The algorithms used are described and related works with different classical methods are presented and commented upon. This chapter is useful in tackling the problem of co-clustering under the mixture approach.
Chapter 2 is devoted to the latent block model proposed in the mixture approach context. The authors discuss this model in detail and present its interest regarding co-clustering. Various algorithms are presented in a general context.
Chapter 3 focuses on binary and categorical data. It presents, in detail, the appropriated latent block mixture models. Variants of these models and algorithms are presented and illustrated using examples.
Chapter 4 focuses on contingency data. Mutual information, phi-squared and model-based co-clustering are studied. Models, algorithms and connections among different approaches are described and illustrated.
Chapter 5 presents the case of continuous data. In the same way, the different approaches used in the previous chapters are extended to this situation.

Table of contents: 

PART I. INTRODUCTION
I.1. Types and Representation of Data

I.1.1. Binary Data

I.1.2. Categorical Data

I.1.3. Continuous Data

I.1.4. Contingency Table

I.1.5. Data Representations

I.2. Simultaneous Analysis

I.2.1. Data Analysis

I.2.2. Co-Clustering

I.2.3. Applications

I.3. Notation
I.4. Different Approaches

I.4.1. Two-Mode Partitioning

I.4.2. Two-Mode Hierarchical Clustering

I.4.3. Direct or Block Clustering

I.4.4. Biclustering

I.4.5. Other Structures and Other Aims

I.5. Model-Based Co-Clustering
I.6. Outline
CHAPTER 1. CLUSTER ANALYSIS
1.1. Introduction
1.2. Miscellaneous Clustering Methods

1.2.1. Hierarchical Approach

1.2.2. The k-Means Algorithm

1.2.3. Other Approaches

1.3. Model-Based Clustering and the Mixture Model
1.4. EM Algorithm

1.4.1. Complete Data and Complete-Data Likelihood

1.4.2. Principle

1.4.3. Application to Mixture Models

1.4.4. Properties

1.4.5. EM as an Alternating Optimization Algorithm

1.5. Clustering and the Mixture Model

1.5.1. The Two Approaches

1.5.2. Classification Likelihood

1.5.3. The CEM Algorithm

1.5.4. Comparison of the Two Approaches

1.5.5. Fuzzy Clustering

1.6. Gaussian Mixture Model

1.6.1. The Model

1.6.2. CEM Algorithm

1.6.3. Spherical Form, Identical Proportions and Volumes

1.6.4. Spherical Form, Identical Proportions but Differing Volumes

1.6.5. Identical Covariance Matrices and Proportions

1.7. Binary Data

1.7.1. Binary Mixture Model

1.7.2. Parsimonious Model

1.7.3. Examples of Application

1.8. Categorical Variables

1.8.1. Multinomial Mixture Model

1.8.2. Parsimonious Model

1.9. Contingency Tables

1.9.1. MNDKI2 Algorithm

1.9.2. Model-Based Approach

1.9.3. Illustration

1.10. Implementation

1.10.1. Choice of Model and of the Number of Classes

1.10.2. Strategies for Use

1.10.3. Extension to Particular Situations

1.11. Conclusion
CHAPTER 2. MODEL-BASED CO-CLUSTERING
2.1. Metric Approach
2.2. Probabilistic Models
2.3. Latent Block Model

2.3.1. Definition

2.3.2. Link with the Mixture Model

2.3.3. Log-Likelihoods

2.3.4. A Complex Model

2.4. Maximum Likelihood Estimation and Algorithms

2.4.1. Variational EM Approach

2.4.2. Classification EM Approach

2.4.3. Stochastic EM-Gibbs Approach

2.5. Bayesian Approach
2.6. Conclusion and Miscellaneous Developments
CHAPTER 3. CO-CLUSTERING OF BINARY AND CATEGORICAL DATA
3.1. Example and Notation
3.2. Metric Approach
3.3. Bernoulli Latent Block Model and Algorithms

3.3.1. The Model

3.3.2. Model Identifiability

3.3.3. Binary LBVEM and LBCEM Algorithms

3.4. Parsimonious Bernoulli Latent Block Models
3.5. Categorical Data
3.6. Bayesian Inference
3.7. Model Selection

3.7.1. Integrated Completed Log-Likelihood (ICL)

3.7.2. Penalized Information Criteria

3.8. Illustrative Experiments

3.8.1. Townships

3.8.2. Mero

3.9. Conclusion
CHAPTER 4. CO-CLUSTERING OF CONTINGENCY TABLES
4.1. Measures of Association

4.1.1. Phi-Squared Coefficient

4.1.2. Mutual Information

4.2. Contingency Table Associated with a Couple of Partitions

4.2.1. Associated Distributions

4.2.2. Associated Measures of Association

4.3. Co-Clustering of Contingency Tables

4.3.1. Two Equivalent Approaches

4.3.2. Parameter Modification of Criteria

4.3.3. Co-Clustering with the Phi-Squared Coefficient

4.3.4. Co-Clustering with Mutual Information

4.4. Model-Based Co-Clustering

4.4.1. Block Model for Contingency Tables

4.4.2. Poisson Latent Block Model

4.4.3. Poisson LBVEM and LBCEM Algorithms

4.5. Comparison of All Algorithms

4.5.1. CROKI2 versus CROINFO

4.5.2. CROINFO versus Poisson LBCEM

4.5.3. Poisson LBVEM versus Poisson LBCEM

4.5.4. Behavior of CROKI2, CROINFO, LBCEM, and LBVEM

4.6. Conclusion
CHAPTER 5. CO-CLUSTERING OF CONTINUOUS DATA
5.1. Metric Approach

5.1.1. Measure of Information

5.1.2. Summarized Data Associated with Partitions

5.1.3. Objective Function

5.1.4. CROEUC Algorithm

5.2. Gaussian Latent Block Model

5.2.1. The Model

5.2.2. Gaussian LBVEM and LBCEM Algorithms

5.2.3. Parsimonious Gaussian Latent Block Models

5.3. Illustrative Example
5.4. Gaussian Block Mixture Model

5.4.1. The Model

5.4.2. GBEM Algorithm

5.5. Numerical Experiments

5.5.1. GBEM versus CROEUC and EM

5.5.2. Effect of the Size of Data

5.6. Conclusion

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Tags: Gérard Govaert, Mohamed Nadif, Co Clustering Models, algorithms and applications