Journal
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
Volume 30, Issue 7, Pages 2067-2078Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TNNLS.2018.2876327
Keywords
Cauchy loss function (CLF); grouping effect; noise suppression; similarity matrix; subspace clustering
Categories
Funding
- National Key Research and Development Program of China [2018YFB1107400]
- National Natural Science Foundation of China [61871470, 61761130079, U1604153, 61301230]
- Program for Science and Technology Innovation Talents in Universities of Henan Province [19HASTIT026]
- Australian Research Council [FL-170100117, DP-180103424, IH-180100002]
- Training Program for the Young-Backbone Teachers in Universities of Henan Province [2017GGJS065]
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Subspace clustering is a problem of exploring the low-dimensional subspaces of high-dimensional data. State-ofthe-art approaches are designed by following the model of spectral clustering-based method. These methods pay much attention to learn the representation matrix to construct a suitable similarity matrix and overlook the influence of the noise term on subspace clustering. However, the real data are always contaminated by the noise and the noise usually has a complicated statistical distribution. To alleviate this problem, in this paper, we propose a subspace clustering method based on Cauchy loss function (CLF). Particularly, it uses CLF to penalize the noise term for suppressing the large noise mixed in the real data. This is due to that the CLF's influence function has an upper bound that can alleviate the influence of a single sample, especially the sample with a large noise, on estimating the residuals. Furthermore, we theoretically prove the grouping effect of our proposed method, which means that highly correlated data can he grouped together. Finally, experimental results on five real data sets reveal that our proposed method outperforms several representative clustering methods.
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