Nonlinear non-negative matrix factorization with fractional power inner-product kernel for face recognition

摘要

It is known that a fractional power polynomial cannot necessarily serve as a Mercer kernel function because it does not ensure to generate a positive semi-definite Gram matrix. This paper constructs a fractional power inner-product function which is theoretically shown to be a Mercer kernel function and presents a novel nonlinear non-negative feature representation approach by integrating kernel non-negative matrix factorization (KNMF) and fractional power inner-product kernel (FPK) for face recognition. The proposed fractional power inner-product kernel NMF (FPKNMF) is based on the cost function with squared Frobenius norm. The update rules of FPKNMF are derived out by means of gradient descent method in reproducing kernel Hilbert space (RKHS). We experimentally analyze the convergence and the performance of our FPKNMF method. Compared with some state of the art kernel based methods on ORL and FERET face databases, experimental results demonstrate that the proposed FPKNMF algorithm has superior performance.