Abstract-We present several new variations on the theme of nonnegative matrix factorization (NMF). Considering factorizations of the form X ¼ F G 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.
Ding et al. REF proposed a semi-nonnegative algorithm where only one matrix factor is restricted to contain nonnegative entries, while it relaxes the constraint on the basis vectors.
Convex and Semi-Nonnegative Matrix Factorizations
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
Computer Science Medicine