Adapting K-Medians to Generate Normalized Cluster Centers

Many applications of clustering require the use of normalized data, such as text or mass spectra mining. The spherical K-means algorithm [6], an adaptation of the traditional K-means algorithm, is highly useful for data of this kind because it produces normalized cluster centers. The K-medians clustering algorithm is also an important clustering tool because of its wellknown resistance to outliers. K-medians, however, is not trivially adapted to produce normalized cluster centers. We introduce a new algorithm (called MN), inspired by spherical K-means, that integrates with Kmedians clustering to produce locally optimal normalized cluster centers. We then show theoretically and experimentally that MN produces clusters of significantly higher quality than one would obtain via a simple scaling of the cluster centers produced from traditional K-medians.