# Revisiting Deep Generalized Canonical Correlation Analysis

arXiv: https://arxiv.org/abs/2312.13455 · HTML: https://mlsanity.com/paper/2312.13455/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 40 references that are in the map.
- First posted on arXiv 20 Dec 2023.

## Builds on (most cited first, 13 of 13)

- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [Exploring Simple Siamese Representation Learning](https://mlsanity.com/paper/2011.10566/) (2020)
- [Barlow Twins: Self-Supervised Learning via Redundancy Reduction](https://mlsanity.com/paper/2103.03230/) (2021)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Self-Supervised Learning with Data Augmentations Provably Isolates Content from Style](https://mlsanity.com/paper/2106.04619/) (2021)
- [Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learning](https://mlsanity.com/paper/1805.08651/) (2018)
- [On Deep Multi-View Representation Learning: Objectives and Optimization](https://mlsanity.com/paper/1602.01024/) (2016)
- [Deep Variational Canonical Correlation Analysis](https://mlsanity.com/paper/1610.03454/) (2016)
- [Understanding Latent Correlation-Based Multiview Learning and Self-Supervision: An Identifiability Perspective](https://mlsanity.com/paper/2106.07115/) (2021)
- [Deep Generalized Canonical Correlation Analysis](https://mlsanity.com/paper/1702.02519/) (2017)
- [Nonparametric Canonical Correlation Analysis](https://mlsanity.com/paper/1511.04839/) (2015)
- [Generalized Canonical Correlation Analysis: A Subspace Intersection Approach](https://mlsanity.com/paper/2003.11205/) (2020)
- [Deep Correlation Analysis for Audio-EEG Decoding](https://mlsanity.com/paper/2105.08492/) (2021)

## Built on by (most cited first, 6 of 6)

- [Identifiable Shared Component Analysis of Unpaired Multimodal Mixtures](https://mlsanity.com/paper/2409.19422/) (2024)
- [Content-Style Learning from Unaligned Domains: Identifiability under Unknown Latent Dimensions](https://mlsanity.com/paper/2411.03755/) (2024)
- [Content-Style Identification via Differential Independence](https://mlsanity.com/paper/2605.17827/) (2026)
- [Unsupervised discovery of the shared and private geometry in multi-view data](https://mlsanity.com/paper/2408.12091/) (2024)
- [Provable Affine Identifiability of Nonlinear CCA under Latent Distributional Priors](https://mlsanity.com/paper/2510.04758/) (2025)
- [Provable Subspace Identification of Nonlinear Multi-view CCA](https://mlsanity.com/paper/2602.23785/) (2026)

## Abstract (arXiv)

Canonical correlation analysis (CCA) is a classic statistical method for discovering latent co-variation that underpins two or more observed random vectors. Several extensions and variations of CCA have been proposed that have strengthened our capabilities in terms of revealing common random factors from multiview datasets. In this work, we first revisit the most recent deterministic extensions of deep CCA and highlight the strengths and limitations of these state-of-the-art methods. Some methods allow trivial solutions, while others can miss weak common factors. Others overload the problem by also seeking to reveal what is not common among the views -- i.e., the private components that are needed to fully reconstruct each view. The latter tends to overload the problem and its computational and sample complexities. Aiming to improve upon these limitations, we design a novel and efficient formulation that alleviates some of the current restrictions. The main idea is to model the private components as conditionally independent given the common ones, which enables the proposed compact formulation. In addition, we also provide a sufficient condition for identifying the common random factors. Judicious experiments with synthetic and real datasets showcase the validity of our claims and the effectiveness of the proposed approach.