Canonical Correlation

@inproceedings{Hair2016CanonicalC,
  title={Canonical Correlation},
  author={Joe F. Hair and Rolph E. Anderson and Ronald L. Tatham and William C. Black},
  year={2016}
}
Suppose you have given a group of students two tests of ten questions each and wish to determine the overall correlation between these two tests. Canonical correlation finds a weighted average of the questions from the first test and correlates this with a weighted average of the questions from the second test. The weights are constructed to maximize the correlation between these two averages. This correlation is called the first canonical correlation coefficient. 

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