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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Kirk Lecture: Bridging the Divide: from Matrix to
Tensor algebra for Optimal Approximation and Compr
ession - Misha Kilmer (Tufts University)
DTSTART;TZID=Europe/London:20230602T160000
DTEND;TZID=Europe/London:20230602T170000
UID:TALK201514AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/201514
DESCRIPTION:Tensors\, also known as multiway arrays\, have bec
ome ubiquitous as representations for operators or
as convenient schemes for storing data. Yet\, whe
n it comes to compressing these objects or analyzi
ng the data stored in them\, the tendency is to ``
flatten&rdquo\; or ``matricize&rdquo\; the data an
d employ traditional linear algebraic tools\, igno
ring higher dimensional correlations/structure tha
t could have been exploited. Impediments to the de
velopment of equivalent tensor-based approaches st
em from the fact that familiar concepts\, such as
rank and orthogonal decomposition\, have no straig
htforward analogues and/or lead to intractable com
putational problems for tensors of order three and
higher. In this talk\, we will review some of the
common tensor decompositions and discuss their th
eoretical and practical limitations. We then discu
ss a family of tensor algebras based on a new defi
nition of tensor-tensor products. Unlike other ten
sor approaches\, the framework we derive based aro
und this tensor-tensor product allows us to genera
lize in a very elegant way all classical algorithm
s from linear algebra. Furthermore\, under our fra
mework\, tensors can be decomposed in a natural (e
.g. &lsquo\;matrix-mimetic&rsquo\;) way with prova
ble approximation properties and with provable ben
efits over traditional matrix approximation. In ad
dition to several examples from recent literature
illustrating the advantages of our tensor-tensor p
roduct framework in practice\, we highlight intere
sting open questions and directions for future res
earch.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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