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Entropy 2016, 18(5), 182; doi:10.3390/e18050182

Entropy-Based Incomplete Cholesky Decomposition for a Scalable Spectral Clustering Algorithm: Computational Studies and Sensitivity Analysis

1
ESAT-STADIUS, Katholieke Universiteit Leuven, Kasteelpark Arenberg 10, B-3001 Leuven, Belgium
2
Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A, B-3001 Leuven, Belgium
*
Author to whom correspondence should be addressed.
Academic Editors: Badong Chen and Jose C. Principe
Received: 3 February 2016 / Revised: 21 April 2016 / Accepted: 9 May 2016 / Published: 13 May 2016
(This article belongs to the Special Issue Information Theoretic Learning)
View Full-Text   |   Download PDF [1917 KB, uploaded 13 May 2016]   |  

Abstract

Spectral clustering methods allow datasets to be partitioned into clusters by mapping the input datapoints into the space spanned by the eigenvectors of the Laplacian matrix. In this article, we make use of the incomplete Cholesky decomposition (ICD) to construct an approximation of the graph Laplacian and reduce the size of the related eigenvalue problem from N to m, with m N . In particular, we introduce a new stopping criterion based on normalized mutual information between consecutive partitions, which terminates the ICD when the change in the cluster assignments is below a given threshold. Compared with existing ICD-based spectral clustering approaches, the proposed method allows the reduction of the number m of selected pivots (i.e., to obtain a sparser model) and at the same time, to maintain high clustering quality. The method scales linearly with respect to the number of input datapoints N and has low memory requirements, because only matrices of size N × m and m × m are calculated (in contrast to standard spectral clustering, where the construction of the full N × N similarity matrix is needed). Furthermore, we show that the number of clusters can be reliably selected based on the gap heuristics computed using just a small matrix R of size m × m instead of the entire graph Laplacian. The effectiveness of the proposed algorithm is tested on several datasets. View Full-Text
Keywords: spectral clustering; incomplete Cholesky decomposition; normalized mutual information spectral clustering; incomplete Cholesky decomposition; normalized mutual information
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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. (CC BY 4.0).

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Langone, R.; Van Barel, M.; Suykens, J.A.K. Entropy-Based Incomplete Cholesky Decomposition for a Scalable Spectral Clustering Algorithm: Computational Studies and Sensitivity Analysis. Entropy 2016, 18, 182.

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