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Title: Beyond union of subspaces: Subspace pursuit on Grassmann manifold for data representation

Discovering the underlying structure of a high-dimensional signal or big data has always been a challenging topic, and has become harder to tackle especially when the observations are exposed to arbitrary sparse perturbations. Here in this paper, built on the model of a union of subspaces (UoS) with sparse outliers and inspired by a basis pursuit strategy, we exploit the fundamental structure of a Grassmann manifold, and propose a new technique of pursuing the subspaces systematically by solving a non-convex optimization problem using the alternating direction method of multipliers. This problem as noted is further complicated by non-convex constraints on the Grassmann manifold, as well as the bilinearity in the penalty caused by the subspace bases and coefficients. Nevertheless, numerical experiments verify that the proposed algorithm, which provides elegant solutions to the sub-problems in each step, is able to de-couple the subspaces and pursue each of them under time-efficient parallel computation.
Authors:
 [1] ;  [2] ;  [3]
  1. Tsinghua Univ., Beijing (China). Tsinghua National Lab. for Information Science and Technology Dept. of Electronic Engineering
  2. North Carolina State Univ., Raleigh, NC (United States). Electrical and Computer Engineering Dept.
  3. Tsinghua Univ., Beijing (China). Tsinghua National Lab. for Information Science and Technology Dept. of Electronic Engineering
Publication Date:
Grant/Contract Number:
NA0002576
Type:
Accepted Manuscript
Journal Name:
2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
Additional Journal Information:
Journal Name: 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP); Conference: 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Shanghai (China), 20-25 Mar 2016; Journal ID: ISSN 2379-190X
Research Org:
North Carolina State Univ., Raleigh, NC (United States)
Sponsoring Org:
USDOE National Nuclear Security Administration (NNSA), Office of Nonproliferation and Verification Research and Development (NA-22); National Natural Science Foundation of China (NNSFC)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; parallel computation; robust subspace pursuit; union of subspaces (UoS); Grassmann manifold constrained optimization; non-convex ADMM
OSTI Identifier:
1438403

Shen, Xinyue, Krim, Hamid, and Gu, Yuantao. Beyond union of subspaces: Subspace pursuit on Grassmann manifold for data representation. United States: N. p., Web. doi:10.1109/ICASSP.2016.7472444.
Shen, Xinyue, Krim, Hamid, & Gu, Yuantao. Beyond union of subspaces: Subspace pursuit on Grassmann manifold for data representation. United States. doi:10.1109/ICASSP.2016.7472444.
Shen, Xinyue, Krim, Hamid, and Gu, Yuantao. 2016. "Beyond union of subspaces: Subspace pursuit on Grassmann manifold for data representation". United States. doi:10.1109/ICASSP.2016.7472444. https://www.osti.gov/servlets/purl/1438403.
@article{osti_1438403,
title = {Beyond union of subspaces: Subspace pursuit on Grassmann manifold for data representation},
author = {Shen, Xinyue and Krim, Hamid and Gu, Yuantao},
abstractNote = {Discovering the underlying structure of a high-dimensional signal or big data has always been a challenging topic, and has become harder to tackle especially when the observations are exposed to arbitrary sparse perturbations. Here in this paper, built on the model of a union of subspaces (UoS) with sparse outliers and inspired by a basis pursuit strategy, we exploit the fundamental structure of a Grassmann manifold, and propose a new technique of pursuing the subspaces systematically by solving a non-convex optimization problem using the alternating direction method of multipliers. This problem as noted is further complicated by non-convex constraints on the Grassmann manifold, as well as the bilinearity in the penalty caused by the subspace bases and coefficients. Nevertheless, numerical experiments verify that the proposed algorithm, which provides elegant solutions to the sub-problems in each step, is able to de-couple the subspaces and pursue each of them under time-efficient parallel computation.},
doi = {10.1109/ICASSP.2016.7472444},
journal = {2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)},
number = ,
volume = ,
place = {United States},
year = {2016},
month = {3}
}