Fast tensorial JADE

TL;DR

This paper introduces a fast, consistent tensorial ICA method based on TJADE and k-JADE, with improved computational efficiency and applicability to large-scale data, supported by theoretical proofs and empirical validation.

Contribution

The paper develops a novel tensorial ICA algorithm that is faster and maintains statistical properties, extending TJADE and k-JADE with practical tuning and large-scale data application.

Findings

Significant speed improvements over existing methods

Maintains statistical consistency and efficiency

Successfully applied to large-scale video data

Abstract

In this work, we propose a novel method for tensorial independent component analysis. Our approach is based on TJADE and $ k $-JADE, two recently proposed generalizations of the classical JADE algorithm. Our novel method achieves the consistency and the limiting distribution of TJADE under mild assumptions, and at the same time offers notable improvement in computational speed. Detailed mathematical proofs of the statistical properties of our method are given and, as a special case, a conjecture on the properties of $ k $-JADE is resolved. Simulations and timing comparisons demonstrate remarkable gain in speed. Moreover, the desired efficiency is obtained approximately for finite samples. The method is applied successfully to large-scale video data, for which neither TJADE nor $ k $-JADE is feasible. Finally, an experimental procedure is proposed to select the values of a set of tuning parameters.