Efficient online spherical K-means clustering

The spherical k-means algorithm, i.e., the k-means algorithm with cosine similarity, is a popular method for clustering high-dimensional text data. In this algorithm, each document as well as each cluster mean is represented as a high-dimensional unit-length vector. However, it has been mainly used in batch mode. That is, each cluster mean vector is updated, only after all document vectors being assigned, as the (normalized) average of all the document vectors assigned to that cluster. This paper investigates an online version of the spherical k-means algorithm based on the well-known Winner-Take-All competitive learning. In this online algorithm, each cluster centroid is incrementally updated given a document. We demonstrate that the online spherical k-means algorithm can achieve significantly better clustering results than the batch version, especially when an annealing-type learning rate schedule is used. We also present heuristics to improve the speed, yet almost without loss of clustering quality.