The dissimilarity representation is an alternative for the use of features in the recognition of real world objects like images, spectra and time-signal. Instead of an absolute characterization of objects by a set of features, the expert or the system is asked to define a measure that estimates the dissimilarity between pairs of objects. Such a measure may also be defined for structural representations such as strings and graphs. The dissimilarity representation is potentially able to bridge structural and statistical pattern recognition. In this thesis we introduce a new fast Mahalanobis-like metric the “Shape Coefficient” for classification of dissimilarity data. Our approach is inspired by the Geometrical Discriminant Analysis and we have defined decision rules to mimic the behavior of the linear and quadratic classifier. The number of parameters is limited (two per class). We also expand and ameliorate this advantageous and rapid adaptive approach to learn only from dissimilarity representations by using the effectiveness of the Support Vector Machines classifier for real-world classification tasks. Several methods for incorporating dissimilarity representations are presented, investigated and compared to the “Shape Coefficient” in this thesis: • Pekalska and Duin prototype dissimilarity based classifiers; • Haasdonk's kernel based SVM classifier; • KNN classifier. Numerical experiments on artificial and real data show interesting behavior compared to Support Vector Machines and to KNN classifier: (a) lower or equivalent error rate, (b) equivalent CPU time, (c) more robustness with sparse dissimilarity data. The experimental results on real world dissimilarity databases show that the “Shape Coefficient” can be an alternative approach to these known methods and can be as effective as them in terms of accuracy for classification.
