Two-mode Higher-Order Tensor Singular Value Decomposition
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simulations
HOSVD_extend.m
README.md
SymTensor.m
demo.m
jacobi.m
mouter.m
qrj1d.m
tenfact_extend.m
tpm_extend.m
uperm.m

README.md

Two-mode-HOSVD

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.