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Mathematical Problems in Engineering
Volume 2017, Article ID 4787039, 9 pages
Research Article

Subspace Clustering with Sparsity and Grouping Effect

School of Mathematics and Statistics, Xidian University, Xi’an 710126, China

Correspondence should be addressed to Weiwei Wang; nc.ude.naidix.liam@gnawww

Received 6 December 2016; Accepted 6 March 2017; Published 22 March 2017

Academic Editor: Simone Bianco

Copyright © 2017 Binbin Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Subspace clustering aims to group a set of data from a union of subspaces into the subspace from which it was drawn. It has become a popular method for recovering the low-dimensional structure underlying high-dimensional dataset. The state-of-the-art methods construct an affinity matrix based on the self-representation of the dataset and then use a spectral clustering method to obtain the final clustering result. These methods show that sparsity and grouping effect of the affinity matrix are important in recovering the low-dimensional structure. In this work, we propose a weighted sparse penalty and a weighted grouping effect penalty in modeling the self-representation of data points. The experimental results on Extended Yale B, USPS, and Berkeley 500 image segmentation datasets show that the proposed model is more effective than state-of-the-art methods in revealing the subspace structure underlying high-dimensional dataset.