Re-compose a Tensor after tensor factorization

Question

I am trying to decompose a 3D matrix using python library scikit-tensor. I managed to decompose my Tensor (with dimensions 100x50x5) into three matrices. My question is how can I compose the initial matrix again using the decomposed matrix produced with Tensor factorization? I want to check if the decomposition has any meaning. My code is the following: import logging from scipy.io.matlab import loadmat from sktensor import dtensor, cp_als import numpy as np //Set logging to DEBUG to see CP-ALS information logging.basicConfig(level=logging.DEBUG) T = np.ones((400, 50)) T = dtensor(T) P, fit, itr, exectimes = cp_als(T, 10, init='random') // how can I re-compose the Matrix T? TA = np.dot(P.U[0], P.U[1].T) I am using the canonical decomposition as provided from the scikit-tensor library function cp_als. Also what is the expected dimensionality of the decomposed matrices? Select the correct answer from above options

Answer 1

You can simply perform a cross product of matrics. can be expressed using Einstein notation as Code implementation of this problem using NumPy: numpy.einsum('az,bz,cz,dz -> abcd', A, B, C, D) so in your case, you would use numpy.einsum('az,bz->ab', P.U[0], P.U[1]) or, in your 3-matrix case numpy.einsum('az,bz,cz->abc', P.U[0], P.U[1], P.U[2]) sktensor.ktensor.ktensor also have a method totensor() that does exactly this: np.allclose(np.einsum('az,bz->ab', P.U[0], P.U[1]), P.totensor()) >>> True If you want to be build successful data science career then enroll for best data science certification. Hope this answer helps.