On the relationship between squared canonical correlation and matrix norm
Conference
Hayashi, K, Yuan, KH, Liang, L. (2017). On the relationship between squared canonical correlation and matrix norm
. 196 141-150. 10.1007/978-3-319-56294-0_13
Hayashi, K, Yuan, KH, Liang, L. (2017). On the relationship between squared canonical correlation and matrix norm
. 196 141-150. 10.1007/978-3-319-56294-0_13
In research on approximating factor analysis (FA) by principal component analysis (PCA), FA loadings and PCA loadings are typically compared using some measure of closeness or distance. Previous studies have used the average squared canonical correlation (ASCC) between the two loading matrices as a measure of closeness. This measure has the advantages of being invariant with respect to sign and column changes, and most conveniently, it is not affected by rotations. However, the drawback of ASCC is that it is hard to intuitively perceive the size of the distance between the (elements of) two loading matrices. Therefore, other measures of difference between matrices such as the Frobenius norm are sometimes preferred. However, then complexities might occur such as the sign changes and the column alignment of the corresponding factors/components as well as rotational indeterminacy. The current study aims to characterize the relationship between the ASCC and a direct measure derived from matrix norms (e.g., Frobenius norm), which facilitates the understanding of the closeness between PCA and FA.
