Unsupervised Feature Selection for the $k$-means Clustering Problem

Part of Advances in Neural Information Processing Systems 22 (NIPS 2009)

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Christos Boutsidis, Petros Drineas, Michael W. Mahoney


We present a novel feature selection algorithm for the $k$-means clustering problem. Our algorithm is randomized and, assuming an accuracy parameter $\epsilon \in (0,1)$, selects and appropriately rescales in an unsupervised manner $\Theta(k \log(k / \epsilon) / \epsilon^2)$ features from a dataset of arbitrary dimensions. We prove that, if we run any $\gamma$-approximate $k$-means algorithm ($\gamma \geq 1$) on the features selected using our method, we can find a $(1+(1+\epsilon)\gamma)$-approximate partition with high probability.