Large-Scale High-Dimensional Clustering with Fast Sketching

In this paper, we address the problem of high-dimensional k-means clustering in a large-scale setting, i.e. for datasets that comprise a large number of items. Sketching techniques have already been used to deal with this “large-scale” issue, by compressing the whole dataset into a single vector of random nonlinear generalized moments from which the $k$ centroids are then retrieved efficiently. However, this approach usually scales quadratically with the dimension; to cope with high-dimensional datasets, we show how to use fast structured random matrices to compute the sketching operator efficiently. This yields significant speed-ups and memory savings for high-dimensional data, while the clustering results are shown to be much more stable, both on artificial and real datasets.