khatri_rao(matrices, weights=None, skip_matrix=None, reverse=False, mask=None)
Khatri-Rao product of a list of matrices
This can be seen as a column-wise kronecker product. (see [R31] for more details).
If one matrix only is given, that matrix is directly returned.
matrices : 2D-array list
list of matrices with the same number of columns, i.e.:
for i in len(matrices): matrices[i].shape = (n_i, m)
weights : 1D-array
array of weights for each rank, of length m, the number of column of the factors (i.e. m == factor[i].shape for any factor)
skip_matrix : None or int, optional, default is None
if not None, index of a matrix to skip
reverse : bool, optional
if True, the order of the matrices is reversed
khatri_rao_product: matrix of shape
prod(n_i) = prod([m.shape for m in matrices])i.e. the product of the number of rows of all the matrices in the product.
A more intuitive but slower implementation is:
kr_product = np.zeros((n_rows, n_columns)) for i in range(n_columns): cum_prod = matrices[:, i] # Accumulates the khatri-rao product of the i-th columns for matrix in matrices[1:]: cum_prod = np.einsum('i,j->ij', cum_prod, matrix[:, i]).ravel() # the i-th column corresponds to the kronecker product of all the i-th columns of all matrices: kr_product[:, i] = cum_prod return kr_product