gemmr.generative_model._generate_random_dominant_subspace_rotations

gemmr.generative_model._generate_random_dominant_subspace_rotations(U, V, m, qx, qy, rng, uvrots)

Generates random weight vectors in the dominant subspaces (of dimension qx and qy).

Separately for X and Y, random rotation matrices are obtained via QR decomposition of a matrix with random entries drawn from a standard normal distribution and choosing the Q factor; the basis vectors U (for X) and V (for Y are then multiplied by these rotation matrices and the first m columns are selected and returned.

Parameters:

• U (np.ndarray(px, px)) – basis vectors for X
• V (np.ndarray(py, py)) – basis vectors for Y
• m (int) – number of between-set association modes
• qx (int) – the dimensionality of the “dominant” subspace for X
• qy (int) – the dimensionality of the “dominant” subspace for Y
• rng (random number generator instance) –
• uvrots (IGNORED) – present for signature compatibility with _generate_dominant_subspace_rotations_from_opti()

Returns:

• U_dominant (np.ndarray (px, m)) – weight vectors for X living in “dominant” subspace
• V_dominant (np.ndarray (py, m)) – weight vectors for Y living in “dominant subspace