Two-mode Higher-Order Tensor Singular Value Decomposition
The main function is HOSVD_extend.m. It implements the two-mode HOSVD algorithm described in https://arxiv.org/abs/1612.03839. The algorithm efficiently approximates the robust eigenvalue/vector pairs for a nearly orthogonal and symmetric tensor of order p. Compared to existing decomposition algorithms based on power iteration or joint diagonalization, our algorithm recovers the components more accurately from a noisy input tensor. For graphical model applications, order-3 tensors are of main interest, for which we improve the perturbation tolerance from 1/d to 1/sqrt(d).
tenfact_extend.m implements the joint diagonalization algorithm (Kuleshov et al AISTATS 2015). We optimized the original algorithm and extended it to allow order-p tensors.
tmp_extend.m implements the power iteration algorithm (Anandkumar et al JMLR 2014) . We optimized the original algorithm and extended it to allow order-p tensors.
See demo.m for input/output format.