Properties of the singular value decomposition for efficient data clustering

We introduce some interesting properties of the singular value decomposition (SVD), and illustrate how they may be used in conjunction with the k-means algorithm for efficiently clustering a set of vectors. Specifically, we use the SVD to preprocess and sort the data vectors, and then use the k-means algorithm on the modified vectors. To illustrate the effectiveness of this approach, we compare it to the k-means algorithm without preprocessing and show that significant gains in clustering speed may be realized.