Blind Determination of the Number of Sources Using Distance Correlation

TL;DR

This paper introduces a new blind method for estimating the number of sources in noisy linear mixtures using distance correlation, which leverages source independence and non-Gaussianity for improved robustness and accuracy.

Contribution

It proposes the Sources' Dependency Criterion (SDC) based on distance correlation, offering a more robust and stable estimate of source count compared to existing methods.

Findings

Demonstrates superior performance over state-of-the-art estimates

Shows robustness against noise covariance variations

Provides stable estimates regardless of mixing matrix changes

Abstract

A novel blind estimate of the number of sources from noisy, linear mixtures is proposed. Based on Sz\'ekely et al.'s distance correlation measure, we define the Sources' Dependency Criterion (SDC), from which our estimate arises. Unlike most previously proposed estimates, the SDC estimate exploits the full independence of the sources and noise, as well as the non-Gaussianity of the sources (as opposed to the Gaussianity of the noise), via implicit use of high-order statistics. This leads to a more robust, resilient and stable estimate w.r.t. the mixing matrix and the noise covariance structure. Empirical simulation results demonstrate these virtues, on top of superior performance in comparison with current state of the art estimates.