BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Elizaveta Rebrova (UCLA) DTSTART:20200627T153000Z DTEND:20200627T163000Z DTSTAMP:20260423T035908Z UID:OAGAS/22 DESCRIPTION:Title: M odewise methods for tensor dimension reduction\nby Elizaveta Rebrova ( UCLA) as part of Online asymptotic geometric analysis seminar\n\n\nAbstrac t\nAlthough tensors are a natural multi-modal extension of matrices\, goin g 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 mos t 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-r ank tensors. Namely\, I will discuss how modewise randomized projections c an preserve tensor geometry in the subspace oblivious way (that is\, a pro jection model is not adapted for a particular tensor subspace). Modewise m ethods are especially interesting for the tensors as they preserve the mul ti-modal structure of the data\, acting on a tensor directly\, without ini tial conversion of tensors to matrices or vectors. I will also discuss an application for the least squares fitting CP model for tensors. Based on o ur joint work with Mark Iwen\, Deanna Needell\, and Ali Zare.\n LOCATION:https://researchseminars.org/talk/OAGAS/22/ END:VEVENT END:VCALENDAR