A statistical approach to class separability

Abstract

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. Copyright © 2005 John Wiley & Sons, Ltd.