This paper proposes a novel dense correspondence method based on generalized unsupervised learning. First, multilayer perceptron (MLP) and residual network are constructed to learn deep point features. Secondly, the approximate geodesic distance of the point cloud is calculated and a feature embedding space is established through feature decomposition. By employing the attention mechanism, it effectively learns the generalized basis function representation. Furthermore, the proposed method combines point features with generalized basis function to generate deep feature representations of 3D shapes. Finally, an unsupervised function mapping network is constructed to obtain dense corresponding representations between shapes. We also propose a tri-regularization mechanism that combines reconstruction loss, descriptor loss, and distance loss for shape matching, effectively improving learning performance and shape corresponding accuracy from the feature and spatial domains. Extensive experimental results have shown that the generalized basis function representation and unsupervised functional map learning mechanism are suitable for arbitrary 3D shapes, breaking through the limitations of previous methods on continuous 2D manifolds, it achieves better performance in arbitrary 3D shape matching.