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Mathematical Problems in Engineering
Volume 2016 (2016), Article ID 9264561, 9 pages
Research Article

Spectral Nonlinearly Embedded Clustering Algorithm

1School of Information and Electrical Engineering, China University of Mining and Technology, Xuzhou, Jiangsu 221116, China
2School of Computer Science and Technology, China University of Mining and Technology, Xuzhou, Jiangsu 221116, China

Received 22 November 2015; Revised 16 May 2016; Accepted 1 June 2016

Academic Editor: Babak Shotorban

Copyright © 2016 Mingming Liu 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.


As is well known, traditional spectral clustering (SC) methods are developed based on the manifold assumption, namely, that two nearby data points in the high-density region of a low-dimensional data manifold have the same cluster label. But, for some high-dimensional and sparse data, such an assumption might be invalid. Consequently, the clustering performance of SC will be degraded sharply in this case. To solve this problem, in this paper, we propose a general spectral embedded framework, which embeds the true cluster assignment matrix for high-dimensional data into a nonlinear space by a predefined embedding function. Based on this framework, several algorithms are presented by using different embedding functions, which aim at learning the final cluster assignment matrix and a transformation into a low dimensionality space simultaneously. More importantly, the proposed method can naturally handle the out-of-sample extension problem. The experimental results on benchmark datasets demonstrate that the proposed method significantly outperforms existing clustering methods.