Joint canonical polyadic decomposition of two tensors with one shared loading matrix

We present an algorithm for jointly performing canonical polyadic decomposition (J-CPD) upon two tensors with one shared loading matrix. Target tensors are firstly matricized and factorized into two components each, and a joint nonorthogonal joint diagonalization based scheme is performed secondly to restore the joint Khatri-rao structures of the results obtained in the first step. Lastly, estimates of loading matrices could be obtained by singular value decomposition based scheme. The proposed algorithm could be used to extract common structures shared with different tensors, and such problem would occur in applications that involve joint utilization of multiple datasets or multiple statistics such as covariance and pseudo-covariance. Simulations are provided to examine the performance of the proposed algorithm.