Sparse Nonnegative Matrix Factorization for Clustering
Author(s)
Kim, Jingu
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Abstract
Properties of Nonnegative Matrix Factorization (NMF) as a clustering method are studied by relating
its formulation to other methods such as K-means clustering. We show how interpreting the objective
function of K-means as that of a lower rank approximation with special constraints allows comparisons
between the constraints of NMF and K-means and provides the insight that some constraints can be
relaxed from K-means to achieve NMF formulation. By introducing sparsity constraints on the coefficient
matrix factor in NMF objective function, we in term can view NMF as a clustering method. We tested
sparse NMF as a clustering method, and our experimental results with synthetic and text data shows
that sparse NMF does not simply provide an alternative to K-means, but rather gives much better and
consistent solutions to the clustering problem. In addition, the consistency of solutions further explains
how NMF can be used to determine the unknown number of clusters from data. We also tested with a
recently proposed clustering algorithm, Affinity Propagation, and achieved comparable results. A fast
alternating nonnegative least squares algorithm was used to obtain NMF and sparse NMF.
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Date
2008
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Text
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Technical Report