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In this paper, we propose a point cloud classification method based on graph neural network and manifold learning. Different from the conventional point cloud analysis methods, this paper uses manifold learning algorithms to embed point cloud features for better considering the geometric continuity on the surface. Then, the nature of point cloud can be acquired in low dimensional space, and after being concatenated with features in the original three-dimensional (3D)space, both the capability of feature representation and the classification network performance can be improved. We pro-pose two manifold learning modules, where one is based on locally linear embedding algorithm, and the other is a non-linear projection method based on neural network architecture. Both of them can obtain better performances than the state-of-the-art baseline. Afterwards, the graph model is constructed by using the k nearest neighbors algorithm, where the edge features are effectively aggregated for the implementation of point cloud classification. Experiments show that the proposed point cloud classification methods obtain the mean class accuracy (mA) of 90.2% and the overall accuracy (oA)of 93.2%, which reach competitive performances compared with the existing state-of-the-art related methods.