# Tensor Generalized Canonical Correlation Analysis

arXiv: https://arxiv.org/abs/2302.05277 · HTML: https://mlsanity.com/paper/2302.05277/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 51 references that are in the map.
- First posted on arXiv 10 Feb 2023.

## Builds on (most cited first, 3 of 3)

- [CR-GAN: Learning Complete Representations for Multi-view Generation](https://mlsanity.com/paper/1806.11191/) (2018)
- [Tensor Canonical Correlation Analysis for Multi-view Dimension Reduction](https://mlsanity.com/paper/1502.02330/) (2015)
- [Generalized Canonical Correlation Analysis: A Subspace Intersection Approach](https://mlsanity.com/paper/2003.11205/) (2020)

## Built on by (most cited first, 2 of 2)

- [Functional Generalized Canonical Correlation Analysis for studying multiple longitudinal variables](https://mlsanity.com/paper/2310.07330/) (2023)
- [Two approaches to multiple canonical correlation analysis for repeated measures data](https://mlsanity.com/paper/2510.04457/) (2025)

## Abstract (arXiv)

Regularized Generalized Canonical Correlation Analysis (RGCCA) is a general statistical framework for multi-block data analysis. RGCCA enables deciphering relationships between several sets of variables and subsumes many well-known multivariate analysis methods as special cases. However, RGCCA only deals with vector-valued blocks, disregarding their possible higher-order structures. This paper presents Tensor GCCA (TGCCA), a new method for analyzing higher-order tensors with canonical vectors admitting an orthogonal rank-R CP decomposition. Moreover, two algorithms for TGCCA, based on whether a separable covariance structure is imposed or not, are presented along with convergence guarantees. The efficiency and usefulness of TGCCA are evaluated on simulated and real data and compared favorably to state-of-the-art approaches.