Contents -- Preface -- Notation and basic terminology -- Abbreviations -- 1. Introduction -- 1.1 Recognizing the pattern -- 1.2 Dissimilarities for representation -- 1.3 Learning from examples -- 1.4 Motivation of the use of dissimilarity representations -- 1.5 Relation to kernels -- 1.6 Outline of the book -- 1.7 In summary -- PART 1 Concepts and theory -- 2. Spaces -- 2.1 Preliminaries -- 2.2 A brief look at spaces -- 2.3 Generalized topological spaces -- 2.4 Generalized metric spaces -- 2.5 Vector spaces -- 2.6 Normed and inner product spaces -- 2.6.1 Reproducing kernel Halbert spaces -- 2.7 Indefinite inner product spaces -- 2.7.1 Reproducing kernel Krez'n spaces -- 2.8 Discussion -- 3. Characterization of dissimilarities -- 3.1 Embeddings, tree models and transformations -- 3.1.1 Embeddings -- 3.1.2 Distorted metric embeddings -- 3.2 Tree models for dissimilarities -- 3.3 Useful transformations -- 3.3.1 Transformations in semimetric spaces -- 3.3.2 Direct product spaces -- 3.3.3 Invariance and robustness -- 3.4 Properties of dissimilarity matrices -- 3.4.1 Dissimilarity matrices -- 3.4.2 Square distances and inner products -- 3.5 Linear embeddings of dissimilarities -- 3.5.1 Euclidean embedding -- 3.5.2 Correction of non-Euclidean dissimilarities -- 3.5.3 Pseudo-Euclidean embedding -- 3.5.4 Generalized average variance -- 3.5.5 Projecting new vectors t o an embedded space -- 3.5.6 Reduction of dimension -- 3.5.7 Reduction of complexity -- 3.5.8 A general embedding -- 3.5.9 Spherical embeddings -- 3.6 Spatial representation of dissimilarities -- 3.6.1 FastMap -- 3.6.2 Multidimensional scaling -- 3.6.3 Reduction of complexity -- 3.7 Summary -- 4. Learning approaches -- 4.1 Traditional learning -- 4.1.1 Data bias and model bias -- 4.1.2 Statistical learning -- 4.1.3 Inductive principles -- 4.1.3.1 Empirical risk minimization (ERM).

4.1.3.2 Principles based on Occam's razor -- Structural Risk Minimization (SRM). -- Regularization principle. -- Bayesian inference. -- 4.1.4 Why is the statistical approach not good enough f o r learning from objects? -- 4.2 The role of dissimilarity representations -- 4.2.1 Learned proximity representations -- 4.2.2 Dissimilarity representations: learning -- 4.3 Classification in generalized topological spaces -- 4.4 Classification in dissimilarity spaces -- 4.4.1 Characterization of dissimilarity spaces -- 4.4.2 Classifiers -- 4.5 Classification in pseudo-Euclidean spaces -- 4.6 On generalized kernels and dissimilarity spaces -- 4.6.1 Connection between dissimilarity spaces and pseudo- Euclidean spaces -- 4.7 Discussion -- 5. Dissimilarity measures -- 5.1 Measures depending on feature types -- 5.2 Measures between populations -- 5.2.1 Normal distributions -- 5.2.2 Divergence measures -- 5.2.3 Discrete probability distributions -- 5.3 Dissimilarity measures between sequences -- 5.4 Information-theoretic measures -- 5.5 Dissimilarity measures between sets -- 5.6 Dissimilarity measures in applications -- 5.6.1 Invariance and robustness -- 5.6.2 Example measures -- 5.7 Discussion and conclusions -- PART 2 Practice -- 6. Visualization -- 6.1 Multidimensional scaling -- 6.1.1 First examples -- 6.1.2 Linear and nonlinear methods: ezarnples -- 6.1.3 Implementation -- 6.2 Other mappings -- 6.3 Examples: getting insight into the data -- 6.4 Tree models -- 6.5 Summary -- 7. Further data exploration -- 7.1 Clustering -- 7.1.1 Standard approaches -- 7.1.2 Clustering o n dissimilarity representations -- 7.1.3 Clustering examples for dissimilarity representations -- 7.2 Intrinsic dimension -- 7.3 Sampling density -- 7.3.1 Proposed criteria -- 7.3.2 Experiments with the NIST digits -- 7.4 Summary -- 8. One-class classifiers -- 8.1 General issues.

8.1.1 Construction of one-class classifiers -- 8.1.2 One-class classijiers in feature spaces -- 8.2 Domain descriptors for dissimilarity representations -- 8.2.1 Neighborhood-based OCCs -- 8.2.2 Generalized mean class descriptor -- 8.2.3 Linear programming dissimilarit3 data description -- 8.2.4 More issues on class descriptors -- 8.3 Experiments -- 8.3.1 Experiment I: Condition monitoring -- 8.3.2 Experiment 11: Diseased mucosa in the oral cavity -- 8.3.3 Experiment 111: Heart disease data -- 8.4 Conclusions -- 9. Classification -- 9.1 Proof of principle -- 9.1.1 NN rule us alternative dissimilarity-based classifiers -- 9.1.2 Experiment I: square dissimilarity representations -- 9.1.3 Experiment 11: the dissimilarity space approach -- 9.1.4 Discussion -- 9.2 Selection of the representation set: the dissimilarity space approach -- 9.2.1 Prototype selection methods -- 9.2.2 Experimental setup -- 9.2.3 Results and discussion -- 9.2.4 Conclusions -- 9.3 Selection of the representation set: the embedding ap- proach -- 9.3.1 Prototype selection methods -- 9.3.2 Experiments and results -- 9.3.3 Conclusions -- 9.4 On corrections of dissimilarity measures -- 9.4.1 Going more Euclidean -- 9.4.2 Experimental setup -- 9.4.3 Results and conclusions -- 9.5 A few remarks on a simulated missing value problem -- 9.6 Existence of zero-error dissimilarity-based classifiers -- 9.6.1 Asymptotic separability of classes -- 9.7 Final discussion -- 10. Combining -- 10.1 Combining for one-class classification -- 10.1.1 Combining strategies -- 10.1.2 Data and experimental setup -- 10.1.3 Results and discussion -- 10.1.4 Summary and conclusions -- 10.2 Combining for standard two-class classification -- 10.2.1 Combining strategies -- 10.2.2 Experiments on the handwritten digit set -- 10.2.3 Results -- 10.2.4 Conclusions -- 10.3 Classifier projection space.

10.3.1 Construction and the use of CPS -- 10.4 Summary -- 11. Representation review and recommendat ions -- 11.1 Representation review -- 11.1.1 Three generalization ways -- 11.I .2 Representation formation -- 11.1.3 Generalization capabilities -- 11.2 Practical considerations -- 11.2.1 Clustering -- 11.2.2 One-class classification -- 11.2.3 Classification -- 12. Conclusions and open problems -- 12.1 Summary and contributions -- 12.2 Extensions of dissimilarity representations -- 12.3 Open questions -- Appendix A On convex and concave functions -- Appendix B Linear algebra in vector spaces -- B.l Some facts on matrices in a Euclidean space -- B.2 Some facts on matrices in a pseudo-Euclidean space -- Appendix C Measure and probability -- Appendix D Statistical sidelines -- D.l Likelihood and parameter estimation -- D.2 Expectation-maximization (EM) algorithm -- D.3 Model selection -- D.4 PCA and probabilistic models -- D.4.1 Gaussian model -- D.4.2 A Gaussian mixture model -- D.4.3 PCA -- D.4.4 Probabilistic PCA -- D.4.5 A mixture of probabilistic PCA -- Appendix E Data sets -- E.l Artificial data sets -- E.2 Real-world data sets -- Bibliography -- Index.