Principal component analysis (PCA) based on the Gram matrix.
Parameters
Name
Type
Description
Default
gram
ndarray of shape (N, N) or (N*(N+1)//2,)
The Gram matrix, either as a full (N, N) array or as the upper triangle in a 1-D array of length N*(N+1)//2 (as returned by :func:gram with full=False).
required
tol
float
Tolerance for the eigenvalues to be considered positive.
1e-7
return_us
bool
If True, also return the eigenvectors U and sqrt-eigenvalues s in addition to the PCs.
False
Returns
Name
Type
Description
PCs
ndarray of shape (N, N - 1)
The principal components (PCs) derived from the Gram matrix. Only returned when return_us=False.
U
ndarray of shape (N, N - 1)
Eigenvectors in descending eigenvalue order. Only returned when return_us=True.
s
ndarray of shape (N - 1,)
Square roots of eigenvalues in descending order. Only returned when return_us=True.