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

Journal Article · Tue Mar 01 00:00:00 EST 2016 · 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

DOI:https://doi.org/10.1109/ICASSP.2016.7472444· OSTI ID:1438403

Shen, Xinyue ^[1]; Krim, Hamid ^[2]; Gu, Yuantao ^[3]

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1. Tsinghua Univ., Beijing (China). Tsinghua National Lab. for Information Science and Technology Dept. of Electronic Engineering; CNEC/NC State
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

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.

• Research Organization: North Carolina State Univ., Raleigh, NC (United States)
• Sponsoring Organization: National Natural Science Foundation of China (NNSFC); USDOE National Nuclear Security Administration (NNSA), Office of Nonproliferation and Verification Research and Development (NA-22)
• Grant/Contract Number: NA0002576
• OSTI ID: 1438403
• Journal Information: 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Journal Name: 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP); ISSN 2379-190X
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
Grassmann manifold constrained optimization
non-convex ADMM
parallel computation
robust subspace pursuit
union of subspaces (UoS)