Locality-constrained nonnegative robust shape interaction subspace clustering and its applications |
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| Affiliation: | 1. School of Mathematics and Information Sciences, Nanchang Hangkong University, Nanchang, 330063, China;2. Department of Mathematics, Shanghai University, Shanghai, 200444, China;3. School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, China;1. Institute for Telecommunications Research, School of Information Technology and Mathematical Sciences, University of South Australia, Mawson Lakes, SA 5095, Australia;2. School of Engineering, University of South Australia, Mawson Lakes, SA 5095, Australia;1. Laboratoire Micro-Onde et Radar, Ecole Militaire Polytechnique, P.O. Box 17, 16111 Bordj El Bahri, Algeria;2. Paris Ouest University, LEME EA4416, 50 rue de Sèvres, 92410 Ville d''Avray, France;3. Signal Processing Group, Technische Universität Darmstadt, Merckstr. 25, 64283 Darmstadt, Germany;1. National Laboratory of Pattern Recognition, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, PR China;2. Visual Computing Center of King Abdullah University of Science and Technology, 23955-6900, Saudi Arabia;3. Department of Electrical, Computer, and Systems Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, USA;1. School of Engineering Science, Simon Fraser University, 8888 University Drive, Burnaby, BC, Canada V5A 1S6;2. Faculty of Computer Science & Information Technology, University of Malaya, Kuala Lumpur, Malaysia;3. Department of Electrical Engineering, National Taiwan University of Science and Technology, Taipei, Taiwan;1. Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB, Canada T6G 2V4;2. School of Electrical Engineering, Aalto University, FI-00076 Aalto, Finland |
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| Abstract: | In this paper, we present a locality-constrained nonnegative robust shape interaction (LNRSI) subspace clustering method. LNRSI integrates the local manifold structure of data into the robust shape interaction (RSI) in a unified formulation, which guarantees the locality and the low-rank property of the optimal affinity graph. Compared with traditional low-rank representation (LRR) learning method, LNRSI can not only pursuit the global structure of data space by low-rank regularization, but also keep the locality manifold, which leads to a sparse and low-rank affinity graph. Due to the clear block-diagonal effect of the affinity graph, LNRSI is robust to noise and occlusions, and achieves a higher rate of correct clustering. The theoretical analysis of the clustering effect is also discussed. An efficient solution based on linearized alternating direction method with adaptive penalty (LADMAP) is built for our method. Finally, we evaluate the performance of LNRSI on both synthetic data and real computer vision tasks, i.e., motion segmentation and handwritten digit clustering. The experimental results show that our LNRSI outperforms several state-of-the-art algorithms. |
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| Keywords: | Shape interaction matrix Subspace clustering Motion segmentation Handwritten digit clustering |
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