CANONCOV Canonical covariance analysis (aka partial least squares)
Canonical correlation analysis
[A, B, U, V, R] = canoncov(X, Y, k)
[A, B, U, V, R] = canoncov(X, Y, k, type)
[A, B, U, V, R] = canoncov(X, Y, k, type, resid)
[A, B, U, V, R] = canoncov(X, Y, k, type, resid, corr)
[A, B, U, V, R] = canoncov(X, Y, k, type, resid, corr, Name=Value)
Inputs:
X: Data matrix of size n x p, where
n is the number of data points and
p is the number of features.
Y: Data matrix of size n x q, where
n is the number of data points and
q is the number of features.
k: Number of canonical components (positive integer).
type: Weighted or binary canonical analysis.
"weighted": Weighted canonical analysis (default).
"binary": Binary canonical analysis.
resid: Global residualization (logical scalar).
0: No global residualization.
1: Global residualization via degree correction (default).
corr: Canonical correlation analysis (logical scalar).
0: Canonical covariance analysis (default).
1: Canonical correlation analysis.
Name=[Value] Arguments
(binary canonical analysis only):
See LOYVAIN for all Name=Value options.
Outputs:
A: Canonical coefficients of X (size p x k).
B: Canonical coefficients of Y (size q x k).
U: Canonical components of X (size n x k).
V: Canonical components of Y (size n x k).
R: Canonical covariances or correlations (size k x k).
If type is "weighted", R denotes the actual covariances or
correlations. If type is "binary", R denotes the
normalized covariances or correlations.
Methodological notes:
Weighted canonical correlation or covariance analysis is computed
via singular value decomposition of cross-covariance matrix.
Binary canonical covariance analysis is computed via co-Loyvain
k-means clustering of cross-covariance matrix. This analysis
produces binary orthogonal canonical coefficients.
Binary canonical covariance analysis is computed via co-Loyvain
k-means clustering of _whitened_ cross-covariance matrix. This
analysis produces binary orthogonal canonical coefficients for
the whitened matrix. However, the output coefficients after
dewhitening will, in general, not be binary.
Global residualization is implemented via generalized degree
correction, and converts k-means co-clustering into k-modularity
co-maximization.
See also:
COLOYVAIN, LOYVAIN, RESIDUALN.