  Clustering analysis by nonnegative low-rank approximations has achieved
remarkable progress in the past decade. However, most approximation approaches
in this direction are still restricted to matrix factorization. We propose a
new low-rank learning method to improve the clustering performance, which is
beyond matrix factorization. The approximation is based on a two-step bipartite
random walk through virtual cluster nodes, where the approximation is formed by
only cluster assigning probabilities. Minimizing the approximation error
measured by Kullback-Leibler divergence is equivalent to maximizing the
likelihood of a discriminative model, which endows our method with a solid
probabilistic interpretation. The optimization is implemented by a relaxed
Majorization-Minimization algorithm that is advantageous in finding good local
minima. Furthermore, we point out that the regularized algorithm with Dirichlet
prior only serves as initialization. Experimental results show that the new
method has strong performance in clustering purity for various datasets,
especially for large-scale manifold data.
