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Issue No. 08 - Aug. (2013 vol. 25)
ISSN: 1041-4347
pp: 1760-1771
Yang Yang , The University of Queensland, Brisbane
Yi Yang , Carnegie Mellon University, Pittsburgh
Heng Tao Shen , The University of Queensland, Brisbane
Yanchun Zhang , Victoria University, Melbourne and Chinese Academy of Sciences
Xiaoyong Du , Renmin University of China, Beijing
Xiaofang Zhou , The University of Queensland, Brisbane
Data clustering is one of the fundamental research problems in data mining and machine learning. Most of the existing clustering methods, for example, normalized cut and $(k)$-means, have been suffering from the fact that their optimization processes normally lead to an NP-hard problem due to the discretization of the elements in the cluster indicator matrix. A practical way to cope with this problem is to relax this constraint to allow the elements to be continuous values. The eigenvalue decomposition can be applied to generate a continuous solution, which has to be further discretized. However, the continuous solution is probably mixing-signed. This result may cause it deviate severely from the true solution, which should be naturally nonnegative. In this paper, we propose a novel clustering algorithm, i.e., discriminative nonnegative spectral clustering, to explicitly impose an additional nonnegative constraint on the cluster indicator matrix to seek for a more interpretable solution. Moreover, we show an effective regularization term which is able to not only provide more useful discriminative information but also learn a mapping function to predict cluster labels for the out-of-sample test data. Extensive experiments on various data sets illustrate the superiority of our proposal compared to the state-of-the-art clustering algorithms.
Clustering algorithms, Kernel, Optimization, Integrated circuits, Eigenvalues and eigenfunctions, Educational institutions, Laplace equations, out-of-sample, Nonnegative spectral clustering, discriminative regularization

H. T. Shen, Y. Zhang, X. Zhou, X. Du, Y. Yang and Y. Yang, "Discriminative Nonnegative Spectral Clustering with Out-of-Sample Extension," in IEEE Transactions on Knowledge & Data Engineering, vol. 25, no. , pp. 1760-1771, 2013.
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