Radial Gaussianization with cluster-specific bias compensation

In recent work, Lyu and Simoncelli [1] introduced radial Gaussianization (RG) as a very efficient procedure for transforming n-dimensional random vectors into Gaussian vectors with independent and identically distributed (i.i.d.) components. This entails transforming the norms of the data so that they become chi-distributed with n degrees of freedom. A necessary requirement is that the original data are generated by an isotropic distribution, that is, their probability density function (pdf) is constant over surfaces of n-dimensional spheres (or, more general, n-dimensional ellipsoids). The case of biases in the data, which is of great practical interest, is studied here; as we demonstrate with experiments, there are situations in which even very small amounts of bias can cause RG to fail. This becomes evident especially when the data form clusters in low-dimensional manifolds. To address this shortcoming, we propose a two-step approach which entails (i) first discovering clusters in the data and removing the bias from each, and (ii) performing RG on the bias-compensated data. In experiments with synthetic data, the proposed bias compensation procedure results in significantly better Gaus-sianization than the non-compensated RG method.