# Generalized Canonical Correlation Analysis: A Subspace Intersection Approach

arXiv: https://arxiv.org/abs/2003.11205 · HTML: https://mlsanity.com/paper/2003.11205/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Mar 2020.

## Built on by (most cited first, 11 of 11)

- [Revisiting Deep Generalized Canonical Correlation Analysis](https://mlsanity.com/paper/2312.13455/) (2023)
- [Multi-Way Representation Alignment](https://mlsanity.com/paper/2602.06205/) (2026)
- [Identifiable Shared Component Analysis of Unpaired Multimodal Mixtures](https://mlsanity.com/paper/2409.19422/) (2024)
- [Melodia: Training-Free Music Editing Guided by Attention Probing in Diffusion Models](https://mlsanity.com/paper/2511.08252/) (2025)
- [Tensor Generalized Canonical Correlation Analysis](https://mlsanity.com/paper/2302.05277/) (2023)
- [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)
- [Tensor Train Completion from Fiberwise Observations Along a Single Mode](https://mlsanity.com/paper/2509.18149/) (2025)
- [Subspace Clustering of Subspaces: Unifying Canonical Correlation Analysis and Subspace Clustering](https://mlsanity.com/paper/2509.18653/) (2025)
- [Communication-Efficient Federated Linear and Deep Generalized Canonical Correlation Analysis](https://mlsanity.com/paper/2109.12400/) (2021)
- [Provable Subspace Identification of Nonlinear Multi-view CCA](https://mlsanity.com/paper/2602.23785/) (2026)

## Abstract (arXiv)

Generalized Canonical Correlation Analysis (GCCA) is an important tool that finds numerous applications in data mining, machine learning, and artificial intelligence. It aims at finding `common' random variables that are strongly correlated across multiple feature representations (views) of the same set of entities. CCA and to a lesser extent GCCA have been studied from the statistical and algorithmic points of view, but not as much from the standpoint of linear algebra. This paper offers a fresh algebraic perspective of GCCA based on a (bi-)linear generative model that naturally captures its essence. It is shown that from a linear algebra point of view, GCCA is tantamount to subspace intersection; and conditions under which the common subspace of the different views is identifiable are provided. A novel GCCA algorithm is proposed based on subspace intersection, which scales up to handle large GCCA tasks. Synthetic as well as real data experiments are provided to showcase the effectiveness of the proposed approach.