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SUMMARY:On tensor completion via nuclear norm minimization - Cun-Hui Zhang
 \, Rutgers University\, USA
DTSTART:20140625T134500Z
DTEND:20140625T141500Z
UID:TALK53117@talks.cam.ac.uk
CONTACT:37296
DESCRIPTION:Many problems can be formulated as recovering a low-rank tenso
 r. Although an\nincreasingly common task\, tensor recovery remains a chall
 enging problem because\nof the delicacy associated with the decomposition 
 of higher order tensors. To\novercome these difficulties\, existing approa
 ches often proceed by unfolding tensors\ninto matrices and then apply tech
 niques for matrix completion. We show here that\nsuch matricization fails 
 to exploit the tensor structure and may lead to suboptimal\nprocedure. Mor
 e specifically\, we investigate a convex optimization approach to\ntensor 
 completion by directly minimizing a tensor nuclear norm and prove that thi
 s\nleads to an improved sample size requirement. To establish our results\
 , we develop\na series of algebraic and probabilistic techniques such as c
 haracterization of\nsubdifferetial for tensor nuclear norm and concentrati
 on inequalities for tensor\nmartingales\, which may be of independent inte
 rests and could be useful in other\ntensor related problems.\nJoint work w
 ith Ming Yuan.
LOCATION:Centre for Mathematical Sciences\, Meeting Room 2
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