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Clustering Large Graphs via the Singular Value Decomposition (2004)
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| Venue: | MACHINE LEARNING |
| Citations: | 112 - 2 self |
BibTeX
@INPROCEEDINGS{Drineas04clusteringlarge,
author = {P. Drineas and A. Frieze and R. Kannan and S. Vempala and V. Vinay},
title = {Clustering Large Graphs via the Singular Value Decomposition},
booktitle = {MACHINE LEARNING},
year = {2004},
pages = {9--33},
publisher = {}
}
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Abstract
We consider the problem of partitioning a set of m points in the n-dimensional Euclidean space into k clusters (usually m and n are variable, while k is fixed), so as to minimize the sum of squared distances between each point and its cluster center. This formulation is usually the objective of the k-means clustering algorithm (Kanungo et al. (2000)). We prove that this problem in NP-hard even for k 2, and we consider a continuous relaxation of this discrete problem: find the k-dimensional subspace V that minimizes the sum of squared distances to V of the m points. This relaxation can be solved by computing the Singular Value Decomposition (SVD) of the n matrix A that represents the m points; this solution can be used to get a 2-approximation algorithm for the original problem. We then argue that in fact the relaxation provides a generalized clustering which is useful in its own right. Finally, we
