The existing Kernel Nonnegative Matrix Factorization (KNMF) cannot ensure the non-negativity of the mapped data in the kernel feature space. This is called the nonnegative in-compatible problem of KNMF. To tackle this problem, this paper presents a new methodology to construct Nonnegative Compatible Kernel (NC-Kernel) for face recognition. We obtain a Nonnegative Nonlinear Mapping (NN-Mapping) by using the techniques of symmetric NMF and nonnegative interpolation strategy. The symmetric function generated by the NN-Mapping is proven to be a nonnegative compatible Mercer kernel function. We apply the NC-Kernel to the Kernel Principle Component Analysis (KPCA) and KNMF for face recognition. The ORL and Pain Expression face databases are selected for evaluations. Experimental results indicate our NC-Kernel based methods outperform some RBF or polynomial kernel based algorithms.
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