Robust Density Comparison Using Eigenvalue Decomposition
Omar Arif, A. Patricio · InTech eBooks · 2012
Many problems in various fields require measuring the similarity between two distributions. Often, the distributions are represented through samples and no closed form exists for the distribution, or it is unknown what the best parametrization is for the distribution . Therefore, the traditional approach of first estimating the probability distribution using the samples, then comparing the distance between the two distributions is not feasible. In this chapter, a method to compute the similarity between two distributions, which is robust to noise and outliers, is presented. The method works directly on the samples without requiring the intermediate step of density estimation, although the approach is closely related to density estimation. The method is based on mapping the distributions into a reproducing kernel Hilbert space, where eigenvalue decomposition is performed. Retention of only the top M eigenvectors minimizes the effect of noise on density comparison.