FastGeo - A Histogram Based Approach to Linear Geometric ICA

Abstract

Guided by the principles of neural geometric ICA, we present a new approach to linear geometric ICA based on histograms rather than basis vectors. Considering that the learning process converges to the medians and not the maxima of the underlying distributions restricted to the receptive fields of the corresponding neurons, we observe a considerable improvement in separation quality of different distributions and a sizable reduction in computational cost by a factor of 100 at least. We further explore the accuracy of the algorithm depending on the number of samples and the choice of the mixing matrix. Finally we discuss the problem of high dimensions and how it can be treated with geometrical ICA algorithms.