Dissimilarity measures in feature space

We present a study of the statistical behavior of the dissimilarity measure, 𝒟₅ proposed previously (Desobry, F. and Davy, M., Proc. IEEE ICASSP, 2003), and which results from a machine learning-based quantile estimation approach, namely, a single-class support vector machine. This dissimilarity measure possesses the interesting property of being asymptotically equivalent to the Fisher ratio when dealing with radial Gaussian probability density functions. More generally, it can be efficiently applied to non-connected quantiles, and to noisy data sets, as outliers are taken into account by the SVM. A generalisation of 𝒟₅ is then proposed, which results in the design of a more general class of dissimilarity measures, also defined in feature space and with the same properties.