Data Clustering with Semi-binary Nonnegative Matrix Factorization

Recently, a considerable growth of interest in using Nonnegative Matrix Factorization (NMF) for pattern classification and data clustering has been observed. For nonnegative data (observations, data items, feature vectors) many problems of partitional clustering can be modeled in terms of a matrix factorization into two groups of vectors: the nonnegative centroid vectors and the binary vectors of cluster indicators. Hence our data partitional clustering problem boils down to a semi-binary NMF problem. Usually, NMF problems are solved with an alternating minimization of a given cost function with multiplicative algorithms. Since our NMF problem has a particular characteristics, we apply a different algorithm for updating the estimated factors than commonly-used, i.e. a binary update with simulated annealing steering. As a result, our algorithm outperforms some well-known algorithms for partitional clustering.