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A new kernel method for nonnegative matrix factorization

In this paper, we propose a right kernel nonnegative matrix factorization (RKNMF) model. Different from the kernel NMF (KNMF) model which implements the kernel method at the left hand of the factorization, RKNMF applies the kernel method at the right hand of the factorization. KNMF lifts the original features to a higher dimension space by a nonlinear map to excavate the structures hidden in the data, while RKNMF hopes to excavate the nonlinear structures between the bases and the reduced dimensional representation. Moreover, we present a double kernel NMF (DKNMF) method which is a combination of KNMF and RKNMF. In addition, practical algorithms are presented for RKNMF and DKNMF. The numerical experiments show that RKNMF outperforms NMF on the task of image reconstruction, and RKNMF and DKNMF outperform NMF and KNMF on the task of extracting features.