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Issue No. 09 - Sept. (2017 vol. 29)
ISSN: 1041-4347
pp: 1834-1845
Yang Yang , Center for Future Media
Fumin Shen , Center for Future Media
Zi Huang , School of Information Technology and Electrical Engineering, University of Queensland, St Lucia, QLD, Australia
Heng Tao Shen , Center for Future Media
Xuelong Li , Center for OPTical IMagery Analysis and Learning (OPTIMAL), State Key Laboratory of Transient Optics and Photonics, Xi?an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, Xi’an, Shaanxi, P.R. China
Spectral clustering has been playing a vital role in various research areas. Most traditional spectral clustering algorithms comprise two independent stages (e.g., first learning continuous labels and then rounding the learned labels into discrete ones), which may cause unpredictable deviation of resultant cluster labels from genuine ones, thereby leading to severe information loss and performance degradation. In this work, we study how to achieve discrete clustering as well as reliably generalize to unseen data. We propose a novel spectral clustering scheme which deeply explores cluster label properties, including discreteness, nonnegativity, and discrimination, as well as learns robust out-of-sample prediction functions. Specifically, we explicitly enforce a discrete transformation on the intermediate continuous labels, which leads to a tractable optimization problem with a discrete solution. Besides, we preserve the natural nonnegative characteristic of the clustering labels to enhance the interpretability of the results. Moreover, to further compensate the unreliability of the learned clustering labels, we integrate an adaptive robust module with $_$\ell _{2,p}$_$ loss to learn prediction function for grouping unseen data. We also show that the out-of-sample component can inject discriminative knowledge into the learning of cluster labels under certain conditions. Extensive experiments conducted on various data sets have demonstrated the superiority of our proposal as compared to several existing clustering approaches.
Clustering algorithms, Predictive models, Robustness, Optimization, Matrix decomposition, Biological system modeling, Laplace equations

Y. Yang, F. Shen, Z. Huang, H. T. Shen and X. Li, "Discrete Nonnegative Spectral Clustering," in IEEE Transactions on Knowledge & Data Engineering, vol. 29, no. 9, pp. 1834-1845, 2017.
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