Sparse Nonnegative Matrix Factorization for Clustering 论文

摘要

Properties of Nonnegative Matrix Factorization (NMF) as a clustering method are studied by relating
\nits formulation to other methods such as K-means clustering. We show how interpreting the objective
\nfunction of K-means as that of a lower rank approximation with special constraints allows comparisons
\nbetween the constraints of NMF and K-means and provides the insight that some constraints can be
\nrelaxed from K-means to achieve NMF formulation. By introducing sparsity constraints on the coefficient
\nmatrix factor in NMF objective function, we in term can view NMF as a clustering method. We tested
\nsparse NMF as a clustering method, and our experimental results with synthetic and text data shows
\nthat sparse NMF does not simply provide an alternative to K-means, but rather gives much better and
\nconsistent solutions to the clustering problem. In addition, the consistency of solutions further explains
\nhow NMF can be used to determine the unknown number of clusters from data. We also tested with a
\nrecently proposed clustering algorithm, Affinity Propagation, and achieved comparable results. A fast
\nalternating nonnegative least squares algorithm was used to obtain NMF and sparse NMF.