---
tag: E0WKQ3XBAC
kind: concept
name: Canonical correlation
msc: [62H20]
sources:
  - url: https://en.wikipedia.org/wiki/Canonical_correlation
same_as:
  wikidata: Q115542
  wikipedia: Canonical correlation
---

## Summary

Canonical correlation analysis studies the linear relations between two groups of variables.
It finds a linear combination of each group such that the two combinations have the largest possible [[correlation|0DNN9B6Q2F]].
Further pairs of combinations are found under the condition that they are uncorrelated with the earlier ones.
The resulting correlations are the canonical correlations.

## Explanations

### L1 human

Suppose that for each student there are several test scores and several measures of study habits.
Canonical correlation asks for the mix of scores and the mix of habits that move together most closely.
The correlation between these two best mixes is the first canonical correlation.
With only one variable in each group, it is just the absolute value of the ordinary correlation.