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Sparse subspace clustering via smoothed ℓp minimization

Dong, Wenhua, Wu, Xiao-jun and Kittler, Josef (2019) Sparse subspace clustering via smoothed ℓp minimization Pattern Recognition Letters, 125. pp. 206-211.

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In this letter, we formulate sparse subspace clustering as a smoothed ℓp (0 ˂ p ˂ 1) minimization problem (SSC-SLp) and present a unified formulation for different practical clustering problems by introducing a new pseudo norm. Generally, the use of ℓp (0 ˂ p ˂ 1) norm approximating the ℓ0 one can lead to a more effective approximation than the ℓp norm, while the ℓp-regularization also causes the objective function to be non-convex and non-smooth. Besides, better adapting to the property of data representing real problems, the objective function is usually constrained by multiple factors (such as spatial distribution of data and errors). In view of this, we propose a computationally efficient method for solving the multi-constrained non-smooth ℓp minimization problem, which smooths the ℓp norm and minimizes the objective function by alternately updating a block (or a variable) and its weight. In addition, the convergence of the proposed algorithm is theoretically proven. Extensive experimental results on real datasets demonstrate the effectiveness of the proposed method.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Electronic Engineering
Authors :
Dong, Wenhua
Wu, Xiao-jun
Date : 1 July 2019
Funders : Engineering and Physical Sciences Research Council (EPSRC)
DOI : 10.1016/j.patrec.2019.04.018
Copyright Disclaimer : © 2019. This manuscript version is made available under the CC-BY-NC-ND 4.0 license
Uncontrolled Keywords : Sparse subspace clustering; ℓp minimization; Unified formulation; Alternating Direction Method
Depositing User : Clive Harris
Date Deposited : 06 Jun 2019 14:45
Last Modified : 23 Apr 2020 02:08

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