Andreas Lang

Andreas Lang, Erich Schubert

The k-means clustering algorithm is a popular algorithm that partitions data into k clusters. There are many improvements to accelerate the standard algorithm. Most current research employs upper and lower bounds on point-to-cluster distances and the triangle inequality to reduce the number of distance computations, with only arrays as underlying data structures. These approaches cannot exploit that nearby points are likely assigned to the same cluster. We propose a new k-means algorithm based on the cover tree index, that has relatively low overhead and performs well, for a wider parameter range, than previous approaches based on the k-d tree. By combining this with upper and lower bounds, as in state-of-the-art approaches, we obtain a hybrid algorithm that combines the benefits of tree aggregation and bounds-based filtering.

Erich Schubert, Andreas Lang, Gloria Feher

Spherical k-means is a widely used clustering algorithm for sparse and high-dimensional data such as document vectors. While several improvements and accelerations have been introduced for the original k-means algorithm, not all easily translate to the spherical variant: Many acceleration techniques, such as the algorithms of Elkan and Hamerly, rely on the triangle inequality of Euclidean distances. However, spherical k-means uses Cosine similarities instead of distances for computational efficiency. In this paper, we incorporate the Elkan and Hamerly accelerations to the spherical k-means algorithm working directly with the Cosines instead of Euclidean distances to obtain a substantial speedup and evaluate these spherical accelerations on real data.