Data Analysis -- Contents -- Preface -- Chapter 1. Principal Component Analysis: Application to Statistical Process Control -- 1.1. Introduction -- 1.2. Data table and related subspaces -- 1.2.1. Data and their characteristics -- 1.2.2. The space of statistical units -- 1.2.3. Variables space -- 1.3. Principal component analysis -- 1.3.1. The method -- 1.3.2. Principal factors and principal components -- 1.3.3. Principal factors and principal components properties -- 1.4. Interpretation of PCA results -- 1.4.1. Quality of representations onto principal planes -- 1.4.2. Axis selection -- 1.4.3. Internal interpretation -- 1.4.4. External interpretation: supplementary variables and individuals -- 1.5. Application to statistical process control -- 1.5.1. Introduction -- 1.5.2. Control charts and PCA -- 1.6. Conclusion -- 1.7. Bibliography -- Chapter 2. Correspondence Analysis: Extensions and Applications to the Statistical Analysis of Sensory Data -- 2.1. Correspondence analysis -- 2.1.1. Data, example, notations -- 2.1.2. Questions: independence model -- 2.1.3. Intensity, significance and nature of a relationship between two qualitative variables -- 2.1.4. Transformation of the data -- 2.1.5. Two clouds -- 2.1.6. Factorial analysis of X -- 2.1.7. Aid to interpretation -- 2.1.8. Some properties -- 2.1.9. Relationships to the traditional presentation -- 2.1.10. Example: recognition of three fundamental tastes -- 2.2. Multiple correspondence analysis -- 2.2.1. Data, notations and example -- 2.2.2. Aims -- 2.2.3. MCA and CA -- 2.2.4. Spaces, clouds and metrics -- 2.2.5. Properties of the clouds in CA of the CDT -- 2.2.6. Transition formulae -- 2.2.7. Aid for interpretation -- 2.2.8. Example: relationship between two taste thresholds -- 2.3. An example of application at the crossroads of CA and MCA -- 2.3.1. Data.

2.3.2. Questions: construction of the analyzed table -- 2.3.3. Properties of the CA of the analyzed table -- 2.3.4. Results -- 2.4. Conclusion: two other extensions -- 2.4.1. Internal correspondence analysis -- 2.4.2. Multiple factor analysis (MFA) -- 2.5. Bibliography -- Chapter 3. Exploratory Projection Pursuit -- 3.1. Introduction -- 3.2. General principles -- 3.2.1. Background -- 3.2.2. What is an interesting projection? -- 3.2.3. Looking for an interesting projection -- 3.2.4. Inference -- 3.2.5. Outliers -- 3.3. Some indexes of interest: presentation and use -- 3.3.1. Projection indexes based on entropy measures -- 3.3.2. Projection indexes based on L2 distances -- 3.3.3. Chi-squared type indexes -- 3.3.4. Indexes based on the cumulative empirical function -- 3.4. Generalized principal component analysis -- 3.4.1. Theoretical background -- 3.4.2. Practice -- 3.4.3. Some precisions -- 3.5. Example -- 3.6. Further topics -- 3.6.1. Other indexes, other structures -- 3.6.2. Unsupervised classification -- 3.6.3. Discrete data -- 3.6.4. Related topics -- 3.6.5. Computation -- 3.7. Bibliography -- Chapter 4. The Analysis of Proximity Data -- 4.1. Introduction -- 4.2. Representation of proximity data in a metric space -- 4.2.1. Four illustrative examples -- 4.2.2. Definitions -- 4.3. Isometric embedding and projection -- 4.3.1. An example of computations -- 4.3.2. The additive constant problem -- 4.3.3. The case of observed dissimilarity measures blurred by noise -- 4.4. Multidimensional scaling and approximation -- 4.4.1. The parametric MDS model -- 4.4.2. The Shepard founding heuristics -- 4.4.3. The majorization approach -- 4.4.4. Extending MDS to a semi-parametric setting -- 4.5. A fielded application -- 4.5.1. Principal coordinates analysis -- 4.5.2. Dimensionality for the representation space -- 4.5.3. The scree test.

4.5.4. Recourse to simulations -- 4.5.5. Validation of results -- 4.5.6. The use of exogenous information for interpreting the output configuration -- 4.5.7. Introduction to stochastic modeling in MDS -- 4.6. Bibliography -- Chapter 5. Statistical Modeling of Functional Data -- 5.1. Introduction -- 5.2. Functional framework -- 5.2.1. Functional random variable -- 5.2.2. Smoothness assumption -- 5.2.3. Smoothing splines -- 5.3. Principal components analysis -- 5.3.1. Model and estimation -- 5.3.2. Dimension and smoothing parameter selection -- 5.3.3. Some comments on discretization effects -- 5.3.4. PCA of climatic time series -- 5.4. Linear regression models and extensions -- 5.4.1. Functional linear models -- 5.4.2. Principal components regression -- 5.4.3. Roughness penalty approach -- 5.4.4. Smoothing parameters selection -- 5.4.5. Some notes on asymptotics -- 5.4.6. Generalized linear models and extensions -- 5.4.7. Land use estimation with the temporal evolution of remote sensing data -- 5.5. Forecasting -- 5.5.1. Functional autoregressive process -- 5.5.2. Smooth ARH(1) -- 5.5.3. Locally ARH(1) processes -- 5.5.4. Selecting smoothing parameters -- 5.5.5. Some asymptotic results -- 5.5.6. Prediction of climatic time series -- 5.6. Concluding remarks -- 5.7. Bibliography -- Chapter 6. Discriminant Analysis -- 6.1. Introduction -- 6.2. Main steps in supervised classification -- 6.2.1. The probabilistic framework -- 6.2.2. Sampling schemes -- 6.2.3. Decision function estimation strategies -- 6.2.4. Variables selection -- 6.2.5. Assessing the misclassification error rate -- 6.2.6. Model selection and resampling techniques -- 6.3. Standard methods in supervised classification -- 6.3.1. Linear discriminant analysis -- 6.3.2. Logistic regression -- 6.3.3. The K nearest neighbors method -- 6.3.4. Classification trees.

6.3.5. Single hidden layer back-propagation network -- 6.4. Recent advances -- 6.4.1. Parametric methods -- 6.4.2. Radial basis functions -- 6.4.3. Boosting -- 6.4.4. Support vector machines -- 6.5. Conclusion -- 6.6. Bibliography -- Chapter 7. Cluster Analysis -- 7.1. Introduction -- 7.2. General principles -- 7.2.1. The data -- 7.2.2. Visualizing clusters -- 7.2.3. Types of classification -- 7.2.4. Objectives of clustering -- 7.3. Hierarchical clustering -- 7.3.1. Agglomerative hierarchical clustering (AHC) -- 7.3.2. Agglomerative criteria -- 7.3.3. Example -- 7.3.4. Ward's method or minimum variance approach -- 7.3.5. Optimality properties -- 7.3.6. Using hierarchical clustering -- 7.4. Partitional clustering: the k -means algorithm -- 7.4.1. The algorithm -- 7.4.2. k-means: a family of methods -- 7.4.3. Using the k-means algorithm -- 7.5. Miscellaneous clustering methods -- 7.5.1. Dynamic cluster method -- 7.5.2. Fuzzy clustering -- 7.5.3. Constrained clustering -- 7.5.4. Self-organizing map -- 7.5.5. Clustering variables -- 7.5.6. Clustering high-dimensional datasets -- 7.6. Block clustering -- 7.6.1. Binary data -- 7.6.2. Contingency table -- 7.6.3. Continuous data -- 7.6.4. Some remarks -- 7.7. Conclusion -- 7.8. Bibliography -- Chapter 8. Clustering and the Mixture Model -- 8.1. Probabilistic approaches in cluster analysis -- 8.1.1. Introduction -- 8.1.2. Parametric approaches -- 8.1.3. Non-parametric methods -- 8.1.4. Validation -- 8.1.5. Notation -- 8.2. The mixture model -- 8.2.1. Introduction -- 8.2.2. The model -- 8.2.3. Estimation of parameters -- 8.2.4. Number of components -- 8.2.5. Identifiability -- 8.3. EM algorithm -- 8.3.1. Introduction -- 8.3.2. Complete data and complete-data likelihood -- 8.3.3. Principle -- 8.3.4. Application to mixture models -- 8.3.5. Properties -- 8.3.6. EM: an alternating optimization algorithm.

8.4. Clustering and the mixture model -- 8.4.1. The two approaches -- 8.4.2. Classification likelihood -- 8.4.3. The CEM algorithm -- 8.4.4. Comparison of the two approaches -- 8.4.5. Fuzzy clustering -- 8.5. Gaussian mixture model -- 8.5.1. The model -- 8.5.2. CEM algorithm -- 8.5.3. Spherical form, identical proportions and volumes -- 8.5.4. Spherical form, identical proportions but differing volumes -- 8.5.5. Identical covariance matrices and proportions -- 8.6. Binary variables -- 8.6.1. Data -- 8.6.2. Binary mixture model -- 8.6.3. Parsimonious model -- 8.6.4. Example of application -- 8.7. Qualitative variables -- 8.7.1. Data -- 8.7.2. The model -- 8.7.3. Parsimonious model -- 8.8. Implementation -- 8.8.1. Choice of model and of the number of classes -- 8.8.2. Strategies for use -- 8.8.3. Extension to particular situations -- 8.9. Conclusion -- 8.10. Bibliography -- Chapter 9. Spatial Data Clustering -- 9.1. Introduction -- 9.1.1. The spatial data clustering problem -- 9.1.2. Examples of applications -- 9.2. Non-probabilistic approaches -- 9.2.1. Using spatial variables -- 9.2.2. Transformation of variables -- 9.2.3. Using a matrix of spatial distances -- 9.2.4. Clustering with contiguity constraints -- 9.3. Markov random fields as models -- 9.3.1. Global methods and Bayesian approaches -- 9.3.2. Markov random fields -- 9.3.3. Markov fields for observations and classes -- 9.3.4. Supervised segmentation -- 9.4. Estimating the parameters for a Markov field -- 9.4.1. Supervised estimation -- 9.4.2. Unsupervised estimation with EM -- 9.4.3. Classification likelihood and inertia with spatial smoothing -- 9.4.4. Other methods of unsupervised estimation -- 9.5. Application to numerical ecology -- 9.5.1. The problem -- 9.5.2. The model: Potts field and Bernoulli distributions -- 9.5.3. Estimating the parameters -- 9.5.4. Resulting clustering.

9.6. Bibliography.