CSDL Home IEEE Transactions on Pattern Analysis & Machine Intelligence 2010 vol.32 Issue No.01 - January

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Issue No.01 - January (2010 vol.32)

pp: 45-55

Chris Ding , University of Texas at Arlington, Arlington

Tao Li , Florida International University, Miami

Michael I. Jordan , University of California at Berkeley, Berkeley

ABSTRACT

We present several new variations on the theme of nonnegative matrix factorization (NMF). Considering factorizations of the form X=FG^T, we focus on algorithms in which G is restricted to containing nonnegative entries, but allowing the data matrix X to have mixed signs, thus extending the applicable range of NMF methods. We also consider algorithms in which the basis vectors of F are constrained to be convex combinations of the data points. This is used for a kernel extension of NMF. We provide algorithms for computing these new factorizations and we provide supporting theoretical analysis. We also analyze the relationships between our algorithms and clustering algorithms, and consider the implications for sparseness of solutions. Finally, we present experimental results that explore the properties of these new methods.

INDEX TERMS

Nonnegative matrix factorization, singular value decomposition, clustering.

CITATION

Chris Ding, Tao Li, Michael I. Jordan, "Convex and Semi-Nonnegative Matrix Factorizations",

*IEEE Transactions on Pattern Analysis & Machine Intelligence*, vol.32, no. 1, pp. 45-55, January 2010, doi:10.1109/TPAMI.2008.277REFERENCES