Sparse matrix decompositions for clustering

Clustering can be understood as a matrix decomposition problem, where a feature vector matrix is represented as a product of two matrices, a matrix of cluster centres and a matrix with sparse columns, where each column assigns individual features to one of the cluster centres. This matrix factorisation is the basis of classical clustering methods, such as those based on non-negative matrix factorisation but can also be derived for other methods, such as k-means clustering. In this paper we derive a new clustering method that combines some aspects of both, non-negative matrix factorisation and k-means clustering. We demonstrate empirically that the new approach outperforms other methods on a host of examples.