Co-Clustering Models, Algorithms and Applications

• Main Authors: Govaert, Gérard, Nadif, Mohamed
• Format: eBook
• Language: English
• Published: Newark John Wiley & Sons, Incorporated 2013
• Edition: 1
• Subjects: Cluster analysis
• DOI: 10.1002/9781118649480

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.

Table of Contents:

• 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 LBMs -- 3.5. Categorical data -- 3.6. Bayesian inference -- 3.7. Model selection -- 3.7.1. The 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 table -- 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 the 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
• Cover -- Title page -- Table of Contents -- Acknowledgment -- 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: 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
• 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 -- Bibliography -- Index