Deep Deterministic Nonlinear ICA via Total Correlation Minimization with Matrix-Based Entropy Functional

TL;DR

This paper introduces DDICA, a deep neural network framework for nonlinear blind source separation that uses matrix-based entropy to optimize independence, offering robustness and versatility across various applications.

Contribution

The paper proposes DDICA, a novel deep learning approach that directly optimizes independence with matrix-based entropy, avoiding complex approximations and enhancing robustness in nonlinear ICA tasks.

Findings

Effective separation of independent components demonstrated across multiple applications.

Improved noise robustness compared to traditional ICA methods.

Streamlined training process without variational or adversarial schemes.

Abstract

Blind source separation, particularly through independent component analysis (ICA), is widely utilized across various signal processing domains for disentangling underlying components from observed mixed signals, owing to its fully data-driven nature that minimizes reliance on prior assumptions. However, conventional ICA methods rely on an assumption of linear mixing, limiting their ability to capture complex nonlinear relationships and to maintain robustness in noisy environments. In this work, we present deep deterministic nonlinear independent component analysis (DDICA), a novel deep neural network-based framework designed to address these limitations. DDICA leverages a matrix-based entropy function to directly optimize the independence criterion via stochastic gradient descent, bypassing the need for variational approximations or adversarial schemes. This results in a streamlined training process and improved resilience to noise. We validated the effectiveness and generalizability of DDICA across a range of applications, including simulated signal mixtures, hyperspectral image unmixing, modeling of primary visual receptive fields, and resting-state functional magnetic resonance imaging (fMRI) data analysis. Experimental results demonstrate that DDICA effectively separates independent components with high accuracy across a range of applications. These findings suggest that DDICA offers a robust and versatile solution for blind source separation in diverse signal processing tasks.