Entropy-Based Incomplete Cholesky Decomposition for a Scalable Spectral Clustering Algorithm: Computational Studies and Sensitivity Analysis
ESAT-STADIUS, Katholieke Universiteit Leuven, Kasteelpark Arenberg 10, B-3001 Leuven, Belgium
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
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
. 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
are calculated (in contrast to standard spectral clustering, where the construction of the full
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
instead of the entire graph Laplacian. The effectiveness of the proposed algorithm is tested on several datasets.
This is an open access article distributed under the Creative Commons Attribution License
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MDPI and ACS Style
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.
Langone R, Van Barel M, Suykens JAK. Entropy-Based Incomplete Cholesky Decomposition for a Scalable Spectral Clustering Algorithm: Computational Studies and Sensitivity Analysis. Entropy. 2016; 18(5):182.
Langone, Rocco; Van Barel, Marc; Suykens, Johan A.K. 2016. "Entropy-Based Incomplete Cholesky Decomposition for a Scalable Spectral Clustering Algorithm: Computational Studies and Sensitivity Analysis." Entropy 18, no. 5: 182.
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