To accurately capture the context information of three-dimensional (3D) point cloud shapes and improve the accuracy of segmentation, we propose a method for the co-segmentation of 3D shape clusters using shape similarity. First, a Farthest Point Sampling is performed on the point cloud shape to obtain the centroid point, and a random pick method is used to determine the neighborhood points to construct a spherical neighborhood. Then, the feature aggregation operator is used to encode geometric topological relationships of 3D point cloud. The associated features among the neighborhood is extracted, and a spatial similarity matrix is constructed using the centroid coordinates of each spherical neighborhood. The spatial similarity matrix sums the weighted local features of the shape extracted by the encoder network to complete the collaborative analysis of the 3D shape. Finally, a hierarchical feature extraction network is built to decode the weighted associated features and complete the shape cluster co-segmentation task. Experimental results show that the co-segmentation accuracy of our algorithm on the ShapeNet Part dataset reaches 86.0%. Compared to the k-nearest neighbor algorithm, using the random selection method within a sphere as the neighborhood point sampling strategy can increase the segmentation accuracy of the network by 1.5%. Compared to the use of shared multilayer perceptrons for feature extraction, the use of feature aggregation operators for convolution operations can increase the segmentation accuracy of the network by 5.6%. Moreover, compared to the current mainstream shape segmentation algorithms, the segmentation accuracy of the proposed algorithm is superior.