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Efficient Computation of Low-Rank Approximations to Higher-Order Moments
Tamara Kolda
Sandia National Laboratories, United States of America
We consider the problem of decomposing a data tensor that is naturally expressed as the sum of p symmetric outer products of vectors of length n. For instance, a dth-order empirical moment tensor has such an expression, and there have been examples of this structure arising in machine learning problems. Our goal is to find the best approximate decomposition that is the sum of r symmetric outer products with r « p. We reduce the work and storage from exponential to linear in n, breaking the curse of dimensionality. When p is massive or the data is streaming, we show that stochastic sampling methods can be used to further reduce the complexity. We also show some intriguing finding on the rank of random tensors. This is joint work with PhD candidate Samantha Sherman at the University of Notre Dame.