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2001

Spectral Relaxation for K-means Clustering

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Spectral Relaxation for K-means Clustering
The popular K-means clustering partitions a data set by minimizing a sum-of-squares cost function. A coordinate descend method is then used to nd local minima. In this paper we show that the minimization can be reformulated as a trace maximization problem associated with the Gram matrix of the data vectors. Furthermore, we show that a relaxed version of the trace maximization problem possesses global optimal solutions which can be obtained by computing a partial eigendecomposition of the Gram matrix, and the cluster assignment for each data vectors can be found by computing a pivoted QR decomposition of the eigenvector matrix. As a by-product we also derive a lower bound for the minimum of the sum-of-squares cost function.
Hongyuan Zha, Xiaofeng He, Chris H. Q. Ding, Ming
Added 31 Oct 2010
Updated 31 Oct 2010
Type Conference
Year 2001
Where NIPS
Authors Hongyuan Zha, Xiaofeng He, Chris H. Q. Ding, Ming Gu, Horst D. Simon
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