Symmetric Tensor Decomposition with Subspace Power Method (50 mins + Q&A)

Joe Kileel
University of Texas at Austin
Department of Mathematics and Oden Institute for Computational E

I will discuss a recent method for low-rank CP symmetric tensor decomposition. The key ingredients are Sylvester’s catalecticant method from classical algebraic geometry and the power method from numerical multilinear algebra. In simulations, this method is roughly one order of magnitude faster than existing decomposition algorithms, with similar accuracy. Next, I will state guarantees for the relevant non-convex optimization problem, and robustness results when the tensor is only approximately low-rank. Finally, if the tensor being decomposed is a higher-order moment of data points (as in multivariate statistics), our method may be performed without explicitly forming the moment tensor. This opens the door to very high-dimensional decompositions. Based on joint works with João Pereira, Timo Klock and Tammy Kolda.

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