Refining clusters in high dimensional text data

The k-means algorithm with cosine similarity, also known as the spherical k-means algorithm, is a popular method for clustering document collections. However, spherical k-means can often yield qualitatively poor results, especially for small clusters, say 25-30 documents per cluster, where it tends to get stuck at a local maximum far away from the optimal. In this paper, we present the first-variation principle that refines a given clustering by incrementally moving data points between clusters, thus achieving a higher objective function value. Combining first-variation with spherical k-means yields a powerful ping-pong strategy that often qualitatively improves k-means clustering. We present several experimental results to show that our proposed method works well in clustering high-dimensional and sparse text data. keywords: clustering, high-dimensional, k-means, refinement algorithm, first variation.