Undercomplete Blind Subspace Deconvolution

TL;DR

This paper introduces the undercomplete blind subspace deconvolution problem, reduces it to independent subspace analysis using temporal concatenation, and adapts kernel-based decorrelation methods for efficient solution and analysis.

Contribution

It extends the BSSD framework, reduces it to ISA, and adapts kernel-ICA techniques like KCCA and KGV for solving high-dimensional ISA tasks.

Findings

Kernel-ISA methods effectively handle high-dimensional problems

Derived methods demonstrate advantages in numerical experiments

Kernel decorrelation techniques improve ISA analysis

Abstract

We introduce the blind subspace deconvolution (BSSD) problem, which is the extension of both the blind source deconvolution (BSD) and the independent subspace analysis (ISA) tasks. We examine the case of the undercomplete BSSD (uBSSD). Applying temporal concatenation we reduce this problem to ISA. The associated `high dimensional' ISA problem can be handled by a recent technique called joint f-decorrelation (JFD). Similar decorrelation methods have been used previously for kernel independent component analysis (kernel-ICA). More precisely, the kernel canonical correlation (KCCA) technique is a member of this family, and, as is shown in this paper, the kernel generalized variance (KGV) method can also be seen as a decorrelation method in the feature space. These kernel based algorithms will be adapted to the ISA task. In the numerical examples, we (i) examine how efficiently the emerging higher dimensional ISA tasks can be tackled, and (ii) explore the working and advantages of the derived kernel-ISA methods.