Source code for tensorly.metrics.factors

from scipy.optimize import linear_sum_assignment
from .. import backend as T


[docs]def congruence_coefficient(matrix1, matrix2, absolute_value=True): """Compute the optimal mean (Tucker) congruence coefficient between the columns of two matrices. Another name for the congruence coefficient is the cosine similarity. The congruence coefficient between two vectors, :math:`\\mathbf{v}_1, \\mathbf{v}_2`, is given by .. math:: \\frac{\\mathbf{v}_1^T \\mathbf{v}_1^T}{\\|\\mathbf{v}_1^T\\| \\|\\mathbf{v}_1^T\\|} When we compute the congruence between two matrices, we find the optimal permutation of the columns and return the mean congruence and the permutation. Parameters ---------- matrix1 : tensorly.Tensor matrix2 : tensorly.Tensor absolute_value : bool Whether to take the absolute value of all vector products before finding the optimal permutation. Returns ------- congruence : float permutation : list """ num_cols = T.shape(matrix1)[1] if T.shape(matrix1) != T.shape(matrix2): raise ValueError("Matrices must have same shape") matrix1 = matrix1/T.norm(matrix1, axis=0) matrix2 = matrix2/T.norm(matrix2, axis=0) all_congruences = T.dot(T.transpose(matrix1), matrix2) if absolute_value: all_congruences = T.abs(all_congruences) all_congruences = T.to_numpy(all_congruences) row_ind, col_ind = linear_sum_assignment(-all_congruences) # Use -corr because scipy didn't doesn't support maximising prior to v1.4 indices = dict(zip(row_ind, col_ind)) permutation = [indices[i] for i in range(num_cols)] return all_congruences[row_ind, col_ind].mean(), permutation