Looking at Ext-RESCAL Xk prediction w.r.t. won tensor-util

In my previous blog post "Notes for Ext-Rescal (may 3rd)"[1] I talked about:

Xk = A*R*A.T where A*R*A.T is a prediction for Xk .

Today I am going to use a utility from the Web of Needs to (attempt to) verify this assumption.

tensor-utils.py in won-matcher-rescal/../python/tools/ contains lines 240 to 262. Line 240 states
"TESTING METHOD for rescal algorithm output predict hints"

Line 244 states
# - threshold: write out only those predictions that are above the threshold

Line 249 to 250 show how to create predictions.

# compute prediction array with scores hint_prediction_matrix = np.dot(A,np.dot(R[SparseTensor.CONNECTION_SLICE], A.T)) Following numpy documentation, numpy.dot is for a 2-D array "If both a and b are 2-D arrays, it is matrix multiplication, but using matmul or a @ b is preferred." I also guessed that SparseTensor.CONNECTION_SLICE was 0. A short python program derived from lines 29 and 31 verifies this. class SparseTensor:    CONNECTION_SLICE = 0 print SparseTensor.CONNECTION_SLICE >> 0 A short program to implement lines 249 to 250 would be: import numpy as np  A = np.array([[-0.70710678, 0.70710678], [ 0.52943053, 0.52943053], [ 0.52943053, 0.52943053],[ 0.00206809, 0.00206809]]) R = np.array([np.array([[  5.47627165e-01,  -1.16883182e-16],[ -6.07013365e-17,   1.29500171e-32]]), np.array([[  1.06958431e-03,  -1.65920612e-19], [ -2.28287465e-19,   3.54015545e-35]]), np.array([[  1.74139035e-33,   5.09236793e-17], [  5.09233343e-17,   1.47866314e+00]])]) hint_prediction_matrix = np.dot(A,np.dot(R[0], A.T)) Lines 252 to 253: # choose indices above threshold to keep hint_indices = hint_prediction_matrix > threshold This is like the first paragraph describing theta in "4.4 Solving Relational Learning Tasks" in M. Nickel et al., "A Three-Way Model for Collective Learning on Multi-Relational Data" A short program to implement lines 252 to 253 would be: threshold = 5.99602451e-04 hint_indices = hint_prediction_matrix > threshold print hint_indices >> array([[ True, False, False, False],        [False,  True,  True, False],        [False,  True,  True, False],        [False, False, False, False]], dtype=bool) Lines 252 to 257:    # choose indices above threshold to keep     hint_indices = hint_prediction_matrix > threshold     if not keepScore:         hint_prediction_matrix[hint_indices] = 1     hint_mask_matrix = np.zeros(hint_prediction_matrix.shape)     hint_mask_matrix[hint_indices] = 1 A short program to implement lines 252 to 257 would be: #if not keepScore: #       hint_prediction_matrix[hint_indices] = 1 hint_mask_matrix = np.zeros(hint_prediction_matrix.shape) hint_mask_matrix[hint_indices] = 1 print hint_indices print hint_mask_matrix I am not sure what lines253 and 254 do, so I commented them out (keepScore = True or keepScore=False) and got the same result...