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l0 Motivated Low-Rank Sparse Subspace Clustering

Brbić, Maria; Kopriva, Ivica (2018) l0 Motivated Low-Rank Sparse Subspace Clustering. IEEE Transactions on Cybernetics, 50 (4). pp. 1711-1725. ISSN 2168-2267

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Abstract

In many applications, high-dimensional data points can be well represented by low-dimensional subspaces. To identify the subspaces, it is important to capture a global and local structure of the data which is achieved by imposing low-rank and sparseness constraints on the data representation matrix. In low-rank sparse subspace clustering (LRSSC), nuclear and L1 norms are used to measure rank and sparsity. However, the use of nuclear and L1 norms leads to an overpenalized problem and only approximates the original problem. In this paper, we propose two L0 quasi-norm based regularizations. First, the paper presents regularization based on multivariate generalization of minimax-concave penalty (GMC-LRSSC), which contains the global minimizers of L0 quasi-norm regularized objective. Afterward, we introduce the Schatten-0 (S0) and L0 regularized objective and approximate the proximal map of the joint solutionusing a proximal average method (S0/L0-LRSSC). The resulting nonconvex optimization problems are solved using alternating direction method of multipliers with established convergence conditions of both algorithms. Results obtained on synthetic and four real-world datasets show the effectiveness of GMC-LRSSC and S0/L0-LRSSC when compared to state-of-the-art methods.

Item Type: Article
Uncontrolled Keywords: alternating direction method of multipliers; gmc penalty; L0 regularization; low-rank; sparsity; subspace clustering
Subjects: NATURAL SCIENCES > Mathematics > Numerical Mathematics
TECHNICAL SCIENCES > Computing > Artificial Intelligence
Divisions: Division of Electronics
Projects:
Project titleProject leaderProject codeProject type
Strukturne dekompozicije empirijskih podataka za računalno potpomognutu dijagnostiku bolesti-DEDADIvica KoprivaIP-2016-06-5235HRZZ
Depositing User: Ivica Kopriva
Date Deposited: 26 Feb 2020 11:59
Last Modified: 26 Feb 2020 11:59
URI: http://fulir.irb.hr/id/eprint/5315
DOI: 10.1109/TCYB.2018.2883566

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