The Perturbed Variation

We introduce a new discrepancy measure between two distributions that gives an indication on their similarity. The new measure, termed the Perturbed Variation (PV), gives an intuitive interpretation of similarity; it optimally perturbs the distributions so that they best fit each other. The PV is defined between continuous and discrete distributions, and can be efficiently estimated from samples. We provide bounds on the convergence of the estimated score to its distributional value, as well as robustness analysis of the PV to outliers. A number of possible applications of the score are presented, and its ability to detect similarity is compared with that of other known measures on real data. We also present a new visual tracking algorithm based on the PV, and compare its performance with known tracking algorithms.