Theory and application of entropiograph based I-divergence estimation

This paper addresses the problem of robust classification of mixture densities by using an entropic-graph information divergence estimate; this provides a means to robustly estimate I-divergence without using any explicit probability density function estimation procedure. We previously applied entropic-graph methods to clustering and classification for mixture densities having uniform contamination density. This paper describes an extension of our previous methods to mixture densities with arbitrary contamination density. Under the assumption that at least one of the pdf's can be estimated from a training sample, a binary hypothesis test is proposed for testing whether an independent target sample has identical distribution as the training sample. This test is based on thresholding an entropic-graph I-divergence estimate constructed from the Minimal Spanning Tree (MST) spanning the target sample on a transformed data space.