# Non-linear ICA based on Cramer-Wold metric

## TL;DR

This paper introduces Cramer-Wold ICA, a non-linear source separation method that simplifies the optimization process by replacing adversarial training with a closed-form independence measure, achieving comparable results to existing models.

## Contribution

The paper presents CW-ICA, a novel non-linear ICA approach that eliminates the need for adversarial training by using a closed-form independence measure, simplifying the model.

## Key findings

- CW-ICA achieves results comparable to ANICA.
- CW-ICA removes the need for adversarial training.
- The method simplifies non-linear ICA optimization.

## Abstract

Non-linear source separation is a challenging open problem with many applications. We extend a recently proposed Adversarial Non-linear ICA (ANICA) model, and introduce Cramer-Wold ICA (CW-ICA). In contrast to ANICA we use a simple, closed--form optimization target instead of a discriminator--based independence measure. Our results show that CW-ICA achieves comparable results to ANICA, while foregoing the need for adversarial training.