Summary: In a high-dimensional sample space, the distribution characteristics of samples are complex. It is difficult to accurately describe the local distribution characteristics of samples directly in the original sample space. This paper proposes a multiple discriminant preserving support subspace radial basis function neural networks with graph similarity learning (DPSS-RBFNN) to describe the distribution characteristics of samples in the original high-dimensional space by multiple low-dimensional and simple discriminant preserving subspaces. DPSS-RBFNN includes the discriminant preserving support subspace (DPSS) learning module and the subspace distribution feature extraction (SDFE) module. In the DPSS learning module, the discriminativeness of each attribute and the joint discriminant between attributes are first considered to construct multiple subspaces. The discriminativeness of the features in these subspaces is not lower than that of the original samples. The graph similarity learning is used to measure the similarity of sample distributions between subspaces with different dimensions. Then multiple DPSSs are obtained. In SDFE module, the distribution characteristics of the samples are described by combining the local responses of the feature space extracted by the sub-RBFNN in each DPSS. The experimental results show that the proposed DPSS-RBFNN with few kernels can achieve higher accuracy in the recognition task than state-of-the-art algorithms.