K-means Clustering with Feature Hashing

One of the major problems of K-means is that one must use dense vectors for its centroids, and therefore it is infeasible to store such huge vectors in memory when the feature space is high-dimensional. We address this issue by using feature hashing (Weinberger et al., 2009), a dimension-reduction technique, which can reduce the size of dense vectors while retaining sparsity of sparse vectors. Our analysis gives theoretical motivation and justification for applying feature hashing to Kmeans, by showing how much will the objective ofK-means be (additively) distorted. Furthermore, to empirically verify our method, we experimented on a document clustering task.