Spherical Randomized Gravitational Clustering

Circular data, i.e., data in the form of 'natural' directions or angles are very common in a number of di erent areas such as biological, meteorological, geological, and political sciences. Clustering circular data is not an easy task due to the circular geometry of the data space. Some clustering approaches, such as the spherical k-means, use the cosine distance instead of the euclidean distance in order to measure the di erence between points. In this paper, we propose a variation of the randomized gravitational clustering algorithm in order to deal with circular data. Basically, we use the cosine distance, we modify the gravitational law in order to use the cosine distance and we use geodesics ('straight' lines in curved spaces) in order to move points according to the gravitational dynamic. Our initial experiments indicate that the spherical gravitational clustering algorithm is able to nd clusters in noisy circular data.