A Topological Discriminant Analysis
Rafik Abdesselam · 2019
This chapter proposes a new discriminant approach, called topological discriminant analysis (TDA), which uses a proximity measure in a topological context. The results of any operation of clustering or classification of objects strongly depend on the proximity measure chosen. The concept of topological equivalence uses the basic notion of a local neighbourhood. In a discrimination context, the chapter defines the topological equivalence between the chosen proximity measure and the perfect discrimination measure adapted to the data considered, through the adjacency matrix induced by each measure, and proposes a new topological method of discrimination using this selected proximity measure. It defines a criterion for topological equivalence of discrimination to judge the quality of discrimination. The results of the proposed TDA, associated with the “best” discriminating proximity measure, are compared with those of classical metric models of discrimination, linear discriminant analysis and multinomial logistic regression.