The results of any operation of clustering or classifying of objects are strongly depend on the proximity measure chosen. The user has to select one measure among many existing proximity measures. Yet according to the notion of topological equivalence chosen, some are more or less equivalent. In this paper, we propose a new approach to comparing and classifying proximity measures in a topological structure and a goal of discrimination. The concept of topological equivalence uses the structure of local neighborhood. Then we propose to define the topological equivalence between two proximity measures, in the context of discrimination, through the topological structure induced by each measure. We also propose a criterion for choosing the "best" measure adapted to data considered among some of the most used proximity measures for quantitative data. The choice of the "best" discriminating proximity measure can be verified retrospectively by a supervised learning method type SVM, discriminant analysis or Logistic regression applied in a topological context. The principle of the proposed approach is illustrated using a real quantitative data example with eight conventional proximity measures of literature. Experiments have evaluated the performance of this discriminant topological approach in terms of size and/or dimension of the relevant data and of selecting the "best" discriminant proximity measure.