JADE for Tensor-Valued Observations

TL;DR

This paper extends the JADE independent component analysis method to tensor-valued data, providing theoretical insights and demonstrating its effectiveness through simulations and real data comparisons.

Contribution

The paper introduces a tensor extension of the JADE ICA method, including theoretical properties and empirical validation, advancing analysis of higher-order structured data.

Findings

Tensor JADE outperforms vector-based ICA methods on tensor data.

Theoretical asymptotic properties of the tensor JADE estimator are established.

Simulation and real data experiments confirm the method's superiority.

Abstract

Independent component analysis is a standard tool in modern data analysis and numerous different techniques for applying it exist. The standard methods however quickly lose their effectiveness when the data are made up of structures of higher order than vectors, namely matrices or tensors (for example, images or videos), being unable to handle the high amounts of noise. Recently, an extension of the classic fourth order blind identification (FOBI) specifically suited for tensor-valued observations was proposed and showed to outperform its vector version for tensor data. In this paper we extend another popular independent component analysis method, the joint approximate diagonalization of eigen-matrices (JADE), for tensor observations. In addition to the theoretical background we also provide the asymptotic properties of the proposed estimator and use both simulations and real data to show its usefulness and superiority over its competitors.