This chapter looks at the simultaneous analysis of several (more than two) arrays of variables measured on the same set of individuals. One difficulty to overcome is that there is no canonical definition of a correlation between three or more variables. Also, there is no canonical extension to the correlation between three or more arrays. The commonly accepted idea is to construct a new array by concatenating column-wise the arrays to be analyzed simultaneously and perform a PCA of this large array. It can be shown that, in the case of two arrays, a given choice of metrics for the PCA makes it possible to recover the Canonical Analysis of two arrays. This choice naturally extends to more than two arrays and leads to the construction of Multiple Canonical Analysis.

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Multiple Canonical Correlation Analysis

  • Alain Franc

摘要

This chapter looks at the simultaneous analysis of several (more than two) arrays of variables measured on the same set of individuals. One difficulty to overcome is that there is no canonical definition of a correlation between three or more variables. Also, there is no canonical extension to the correlation between three or more arrays. The commonly accepted idea is to construct a new array by concatenating column-wise the arrays to be analyzed simultaneously and perform a PCA of this large array. It can be shown that, in the case of two arrays, a given choice of metrics for the PCA makes it possible to recover the Canonical Analysis of two arrays. This choice naturally extends to more than two arrays and leads to the construction of Multiple Canonical Analysis.