A statistical approach for separability of classes

D.A. Zighed (1) , Stéphane Lallich (1) , Fabrice Muhlenbach (2)

1 ERIC - Equipe de Recherche en Ingénierie des Connaissances
2 LHC - Laboratoire Hubert Curien

We propose a new statistical approach for characterizing the class separability degree in R^{p}. This approach is based on a non-parametric statistic called the cut edge weight. We show in this paper the principle and the experimental applications of this statistic. First, we build a geometrical connected graph like Toussaint's Relative Neighbourhood Graph on all examples of the learning set. Second, we cut all edges between two examples of a different class. Third, we compute the relative weight of these cut edges. If the relative weight of the cut edges is in the expected range of a random distribution of the labels on all the neighbourhood of the graph's vertices, then no neighbourhood-based method provides a reliable prediction model. We will say then that the classes to predict are non-separable.

Mots clés: separability; supervised learning; computational geometry

Domaines: Apprentissage [cs.LG]

D.A. Zighed, Stéphane Lallich, Fabrice Muhlenbach. A statistical approach for separability of classes. Applied Stochastic Models in Business and Industry, 2005, 21 (2), pp.187-197. ⟨hal-00383773⟩