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

arXiv: https://arxiv.org/abs/2601.00904 · HTML: https://mlsanity.com/paper/2601.00904/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 56 references that are in the map.
- First posted on arXiv 31 Dec 2025.

## Builds on (most cited first, 11 of 11)

- [MINE: Mutual Information Neural Estimation](https://mlsanity.com/paper/1801.04062/) (2018)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [Disentanglement by Nonlinear ICA with General Incompressible-flow Networks (GIN)](https://mlsanity.com/paper/2001.04872/) (2020)
- [Measuring Dependence with Matrix-based Entropy Functional](https://mlsanity.com/paper/2101.10160/) (2021)
- [Optimal Randomized Approximations for Matrix based Renyi's Entropy](https://mlsanity.com/paper/2205.07426/) (2022)
- [Computationally Efficient Approximations for Matrix-based Renyi's Entropy](https://mlsanity.com/paper/2112.13720/) (2021)
- [Simultaneous Non-Gaussian Component Analysis (SING) for Data Integration in Neuroimaging](https://mlsanity.com/paper/2005.00597/) (2020)
- [Deep Deterministic Independent Component Analysis for Hyperspectral Unmixing](https://mlsanity.com/paper/2202.02951/) (2022)
- [Aberrant High-Order Dependencies in Schizophrenia Resting-State Functional MRI Networks](https://mlsanity.com/paper/2310.17445/) (2023)
- [Functional Connectivity via Total Correlation: Analytical results in Visual Areas](https://mlsanity.com/paper/2208.05770/) (2022)
- [Functional Connectome of the Human Brain with Total Correlation](https://mlsanity.com/paper/2210.03231/) (2022)

## Built on by (most cited first, 1 of 1)

- [Isolating Nonlinear Independent Sources in fMRI with β-TCVAE Models](https://mlsanity.com/paper/2605.16708/) (2026)

## Abstract (arXiv)

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.