# A Tutorial on Canonical Correlation Methods

arXiv: https://arxiv.org/abs/1711.02391 · HTML: https://mlsanity.com/paper/1711.02391/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Nov 2017.

## Built on by (most cited first, 14 of 14)

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- [Fair Canonical Correlation Analysis](https://mlsanity.com/paper/2309.15809/) (2023)
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- [A hierarchical Bayesian model to find brain-behaviour associations in incomplete data sets](https://mlsanity.com/paper/2103.06845/) (2021)
- [Inertial Sensor Data To Image Encoding For Human Action Recognition](https://mlsanity.com/paper/2105.13533/) (2021)
- [Dimensionality reduction for prediction: Application to Bitcoin and Ethereum](https://mlsanity.com/paper/2112.15036/) (2021)
- [Higher Order Correlation Analysis for Multi-View Learning](https://mlsanity.com/paper/2201.11949/) (2022)
- [Reinterpreting Economic Complexity: A co-clustering approach](https://mlsanity.com/paper/2406.16199/) (2024)
- [TreeCCA: Canonical Correlation Analysis via Gradient-Boosted Trees](https://mlsanity.com/paper/2607.27027/) (2026)

## Abstract (arXiv)

Canonical correlation analysis is a family of multivariate statistical methods for the analysis of paired sets of variables. Since its proposition, canonical correlation analysis has for instance been extended to extract relations between two sets of variables when the sample size is insufficient in relation to the data dimensionality, when the relations have been considered to be non-linear, and when the dimensionality is too large for human interpretation. This tutorial explains the theory of canonical correlation analysis including its regularised, kernel, and sparse variants. Additionally, the deep and Bayesian CCA extensions are briefly reviewed. Together with the numerical examples, this overview provides a coherent compendium on the applicability of the variants of canonical correlation analysis. By bringing together techniques for solving the optimisation problems, evaluating the statistical significance and generalisability of the canonical correlation model, and interpreting the relations, we hope that this article can serve as a hands-on tool for applying canonical correlation methods in data analysis.