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Computational Intelligence and Neuroscience
Volume 2017 (2017), Article ID 2658707, 14 pages
Research Article

Fast Constrained Spectral Clustering and Cluster Ensemble with Random Projection

1Guangxi Key Laboratory of Cryptogpraphy and Information Security, School of Computer Science and Information Security, Guilin University of Electronic Technology, Guilin 541004, China
2State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China
3State Key Laboratory of Mathematical Engineering and Advanced Computing, Zhengzhou 450002, China
4National University of Defense Technology, Nanjing 210012, China

Correspondence should be addressed to Mao Ye

Received 7 March 2017; Accepted 1 August 2017; Published 25 September 2017

Academic Editor: Diego Andina

Copyright © 2017 Wenfen 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.


Constrained spectral clustering (CSC) method can greatly improve the clustering accuracy with the incorporation of constraint information into spectral clustering and thus has been paid academic attention widely. In this paper, we propose a fast CSC algorithm via encoding landmark-based graph construction into a new CSC model and applying random sampling to decrease the data size after spectral embedding. Compared with the original model, the new algorithm has the similar results with the increase of its model size asymptotically; compared with the most efficient CSC algorithm known, the new algorithm runs faster and has a wider range of suitable data sets. Meanwhile, a scalable semisupervised cluster ensemble algorithm is also proposed via the combination of our fast CSC algorithm and dimensionality reduction with random projection in the process of spectral ensemble clustering. We demonstrate by presenting theoretical analysis and empirical results that the new cluster ensemble algorithm has advantages in terms of efficiency and effectiveness. Furthermore, the approximate preservation of random projection in clustering accuracy proved in the stage of consensus clustering is also suitable for the weighted -means clustering and thus gives the theoretical guarantee to this special kind of -means clustering where each point has its corresponding weight.