Measuring the resemblance between proximity measures in a topological structure
Résumé
Choosing a proximity measure between objects has a direct impact on the results of any operation of comparison or structuring a set of objects. For a given problem, the user is prompted to choose one among the many existing proximity measures. However, some are more or less equivalent. In this paper, we propose to introduce a statistical test for comparing matrices associated with proximity measures based on the concept of neighborhood graphs. It believes that two proximity measures are topological equivalent if they induce the same neighborhood structure on the objects. The comparison matrix is a useful tool for measuring the degree of resemblance between two empirical proximity matrices. Like the Mantel test used to compare two matrices of dissimilarity for measuring the degree of equivalence in preordonnance, the proposed chi-square test compares two adjacency matrix for measuring the degree of equivalence in topology. We compare empirically the two tests for thirteen proximity measures for continuous data from the literature.
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