Data Analysis

Gérard Govaert is Professor at the University of Technology of Compiègne, France. He is also a member of the CNRS Laboratory Heudiasyc (Heuristic and diagnostic of complex systems). His research interests include latent structure modeling, model selection, model-based cluster analysis, block clustering and statistical pattern recognition. He is one of the authors of the MIXMOD (MIXture MODelling) software.

• Preface xiiiChapter 1. Principal Component Analysis: Application to Statistical Process Control 1Gilbert SAPORTA, Ndèye NIANG1.1. Introduction 11.2. Data table and related subspaces 21.3. Principal component analysis 81.4. Interpretation of PCA results 111.5. Application to statistical process control 181.6. Conclusion 221.7. Bibliography 23Chapter 2. Correspondence Analysis: Extensions and Applications to the Statistical Analysis of Sensory Data 25Jérôme PAGÈS2.1. Correspondence analysis 252.2. Multiple correspondence analysis 392.3. An example of application at the crossroads of CA and MCA 502.4. Conclusion: two other extensions 632.5. Bibliography 64Chapter 3. Exploratory Projection Pursuit 67Henri CAUSSINUS, Anne RUIZ-GAZEN3.1. Introduction 673.2. General principles 683.3. Some indexes of interest: presentation and use 713.4. Generalized principal component analysis 763.5. Example 813.6. Further topics 863.7. Bibliography 89Chapter 4. The Analysis of Proximity Data 93Gerard D’AUBIGNY4.1. Introduction 934.2. Representation of proximity data in a metric space 974.3. Isometric embedding and projection 1034.4. Multidimensional scaling and approximation 1084.5. Afielded application 1224.6. Bibliography 139Chapter 5. Statistical Modeling of Functional Data 149Philippe BESSE, Hervé CARDOT5.1. Introduction 1495.2. Functional framework1525.3. Principal components analysis 1565.4. Linear regression models and extensions 1615.5. Forecasting 1695.6. Concluding remarks 1765.7. Bibliography 177Chapter 6. Discriminant Analysis 181Gilles CELEUX6.1. Introduction 1816.2. Main steps in supervised classification 1826.3. Standard methods in supervised classification 1906.4. Recent advances 2046.5. Conclusion 2116.6. Bibliography 212Chapter 7. Cluster Analysis 215Mohamed NADIF, Gérard GOVAERT7.1. Introduction 2157.2. General principles 2177.3. Hierarchical clustering 2247.4. Partitional clustering: the k-means algorithm 2337.5. Miscellaneous clustering methods 2397.6. Block clustering 2457.7. Conclusion 2517.8. Bibliography 251Chapter 8. Clustering and the Mixture Model 257Gérard GOVAERT8.1. Probabilistic approaches in cluster analysis 2578.2. The mixture model 2618.3. EM algorithm 2638.4. Clustering and the mixture model 2678.5.Gaussian mixture model 2718.6. Binary variables 2758.7. Qualitative variables 2798.8. Implementation 2828.9. Conclusion 2848.10. Bibliography 284Chapter 9. Spatial Data Clustering 289Christophe AMBROISE, Mo DANG9.1. Introduction 2899.2. Non-probabilistic approaches 2939.3. Markov random fields as models 2959.4. Estimating the parameters for a Markov field 3059.5. Application to numerical ecology 3139.6. Bibliography 316List of Authors 319Index 323

"The first part of this book is devoted to methods seeking relevantdimensions of data. The variables thus obtained provide a synthetic description which often results in a graphical representation of the data. After a general presentation of the discriminating analysis, the second part is devoted to clustering methods which constitute another method, often complementary to the methods described in the first part, to synthesize and to analyze the data." (Zentralblatt MATH 2016)