Measure Transformed Independent Component Analysis

In this paper we derive a new framework for independent component analysis (ICA), called measure-transformed ICA (MTICA), that is based on applying a structured transform to the probability distribution of the observation vector, i.e., transformation of the probability measure defined on its observation space. By judicious choice of the transform we show that the separation matrix can be uniquely determined via diagonalization of several measure-transformed covariance matrices. In MTICA the separation matrix is estimated via approximate joint diagonalization of several empirical measure-transformed covariance matrices. Unlike kernel based ICA techniques where the transformation is applied repetitively to some affine mappings of the observation vector, in MTICA the transformation is applied only once to the probability distribution of the observations. This results in performance advantages and reduced implementation complexity. Simulations demonstrate the advantages of the proposed approach as compared to other existing state-of-the-art methods for ICA.