Abstract In this paper, we propose a general formulation for kernel nonnegative matrix factorization with flflexible kernels. Specififically, we propose the Gaussian nonnegative matrix factorization (GNMF) algorithm by using the Gaussian kernel in the framework. Different from a recently developed polynomial NMF (PNMF), GNMF fifinds basis vectors in the kernel-induced feature space and the computational cost is independent of input dimensions. Furthermore, we prove the convergence and nonnegativity of decomposition of our method. Extensive experiments compared with PNMF and other NMF algorithms on several face databases, validate the effectiveness of the proposed method