NDLI: Tensor completion via optimization on the product of matrix manifolds

Content Provider	IEEE Xplore Digital Library
Author	Girson, J. Aeron, S.
Copyright Year	2015
Description	Author affiliation: Sch. of Eng., Tufts Univ., Medford, MA, USA (Girson, J.; Aeron, S.)
Abstract	We present a method for tensor completion using optimization on low-rank matrix manifolds. Our notion of tensor-rank is based on the recently proposed framework of tensor- Singular Value Decomposition (t-SVD) in [1], [2]. In contrast to convex optimization methods used in [1] that operate in a high-dimensional space, in the manifold setting, one works directly in the reduced dimensionality space and is thus able to significantly reduce the computational costs [3], [4]. In this paper we focus on 3-D data and under the tensor algebraic framework of [1], [2] we show that a 3-D tensor of fixed tubal-rank can be seen as an element of the product manifold of fixed low-rank matrices in the Fourier domain. The tensor completion problem then reduces to finding the best approximation to the sampled data on this product manifold. Further, for 3-D data we consider and compare recovery performance under two approaches. In the first approach one samples entire mode-3 fibers of the tensor, which we refer to as tubal-sampling. The second approach employs element-wise sampling and we simply refer to this method as sampling. For these two types of sampling approaches, we present simulation results for surveillance video data and show that recovery under random sampling has better performance compared to the random tubal-sampling.
Starting Page	177
Ending Page	180
File Size	547171
Page Count	4
File Format	PDF
e-ISBN	9781479919635
DOI	10.1109/CAMSAP.2015.7383765
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2015-12-13
Publisher Place	Mexico
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Manifolds Tensile stress Convolution Xenon Electron tubes Matrix decomposition Optimization
Content Type	Text
Resource Type	Article

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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