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UID:9b563644b4ef41f0c944a399e9aa0b3f
CATEGORIES:Colloquia
CREATED:20211104T113143
SUMMARY:A new tensor framework - theory and applications
LOCATION:zoom
DESCRIPTION:Abstract:\nTensors (aka multiway arrays) can be instrumental in revealing l
 atent correlations residing in high dimensional spaces. Despite their appli
 cability to a broad range of applications in machine learning, data compres
 sion, and imaging, inconsistencies between tensor and matrix algebra have b
 een complicating their broader utility.  Researchers seeking to overcome th
 ose discrepancies have introduced several different candidate extensions, e
 ach introducing unique advantages and challenges. In this talk, we review s
 ome of the common tensor definitions, discuss their limitations, and introd
 uce our tensor product framework which permits the elegant extension of lin
 ear algebraic concepts and algorithms to tensors.  Following introduction o
 f fundamental tensor operations, we discuss tensor decompositions in furthe
 r depth, including tensor SVDs, based on the tensor product framework which
  can be computed efficiently in parallel.  We present theoretical results r
 egarding compressibility and provide demonstrations of the applicability of
  our theory and algorithms on examples such as model reduction and image re
 presentation.  \n
X-ALT-DESC;FMTTYPE=text/html:<p style="background: white;">Abstract:</p><p style="background: white;">Te
 nsors (aka multiway arrays) can be instrumental in revealing latent correla
 tions residing in high dimensional spaces. Despite their applicability to a
  broad range of applications in machine learning, data compression, and ima
 ging, inconsistencies between tensor and matrix algebra have been complicat
 ing their broader utility.&nbsp; Researchers seeking to overcome those disc
 repancies have introduced several different candidate extensions, each intr
 oducing unique advantages and challenges. In this talk, we review some of t
 he common tensor definitions, discuss their limitations, and introduce our 
 tensor product framework which permits the elegant extension of linear alge
 braic concepts and algorithms to tensors.&nbsp; Following introduction of f
 undamental tensor operations, we discuss tensor decompositions in further d
 epth, including tensor SVDs, based on the tensor product framework which ca
 n be computed efficiently in parallel.&nbsp; We present theoretical results
  regarding compressibility and provide demonstrations of the applicability 
 of our theory and algorithms on examples such as model reduction and image 
 representation.&nbsp;&nbsp;</p>
CONTACT:Misha Kilmer (Tufts University)
DTSTAMP:20260830T071551
DTSTART;TZID=America/New_York:20211110T153000
DTEND;TZID=America/New_York:20211110T163000
SEQUENCE:0
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