# Non-linear Canonical Correlation Analysis: A Compressed Representation Approach

arXiv: https://arxiv.org/abs/1810.13259 · HTML: https://mlsanity.com/paper/1810.13259/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Oct 2018.

## Built on by (most cited first, 4 of 4)

- [A Cookbook of Self-Supervised Learning](https://mlsanity.com/paper/2304.12210/) (2023)
- [Max-Sliced Mutual Information](https://mlsanity.com/paper/2309.16200/) (2023)
- [InfoDPCCA: Information-Theoretic Dynamic Probabilistic Canonical Correlation Analysis](https://mlsanity.com/paper/2506.08884/) (2025)
- [Learning Conditional Expectation Operators via Functional Newton Updates](https://mlsanity.com/paper/2609.35598/) (2026)

## Abstract (arXiv)

Canonical Correlation Analysis (CCA) is a linear representation learning method that seeks maximally correlated variables in multi-view data. Non-linear CCA extends this notion to a broader family of transformations, which are more powerful in many real-world applications. Given the joint probability, the Alternating Conditional Expectation (ACE) algorithm provides an optimal solution to the non-linear CCA problem. However, it suffers from limited performance and an increasing computational burden when only a finite number of samples is available. In this work we introduce an information-theoretic compressed representation framework for the non-linear CCA problem (CRCCA), which extends the classical ACE approach. Our suggested framework seeks compact representations of the data that allow a maximal level of correlation. This way we control the trade-off between the flexibility and the complexity of the model. CRCCA provides theoretical bounds and optimality conditions, as we establish fundamental connections to rate-distortion theory, the information bottleneck and remote source coding. In addition, it allows a soft dimensionality reduction, as the compression level is determined by the mutual information between the original noisy data and the extracted signals. Finally, we introduce a simple implementation of the CRCCA framework, based on lattice quantization.