Modewise methods for tensor dimension reduction

Abstract: Although tensors are a natural multi-modal extension of matrices, going beyond two modes (that is, rows and columns) presents many interesting non-trivialities. For example, the notion of singular values is no longer well-defined, and there are various versions of the rank. One of the most natural (and mathematically challenging) definitions of the tensor rank is so-called CP-rank: for a tensor X, it is a minimal number of rank one tensors whose linear combination constitutes X. Main focus of my talk will be an extension of the celebrated Johnson-Lindenstrauss lemma to low CP-rank tensors. Namely, I will discuss how modewise randomized projections can preserve tensor geometry in the subspace oblivious way (that is, a projection model is not adapted for a particular tensor subspace). Modewise methods are especially interesting for the tensors as they preserve the multi-modal structure of the data, acting on a tensor directly, without initial conversion of tensors to matrices or vectors. I will also discuss an application for the least squares fitting CP model for tensors. Based on our joint work with Mark Iwen, Deanna Needell, and Ali Zare.

analysis of PDEsmetric geometry

Audience: researchers in the topic

Online asymptotic geometric analysis seminar

Series comments: The link: technion.zoom.us/j/99202255210

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