Analyzing point clouds with neural networks is a current research hotspot. In order to analyze the 3D geometric features of point clouds, most neural networks improve the network performance by adding local geometric operators and trainable parameters. However, deep learning usually requires a large amount of computational resources for training and inference, which poses challenges to hardware devices and energy consumption. Therefore, some researches have started to try to use a nonparametric approach to extract features. Point-NN combines nonparametric modules to build a nonparametric network for 3D point cloud analysis, and the nonparametric components include operations such as trigonometric embedding, farthest point sampling (FPS), k-nearest neighbor (k-NN), and pooling. However, Point-NN has some blindness in feature embedding using the trigonometric function during feature extraction. To eliminate this blindness as much as possible, we utilize a nonparametric energy function-based attention mechanism (ResSimAM). The embedded features are enhanced by calculating the energy of the features by the energy function, and then the ResSimAM is used to enhance the weights of the embedded features by the energy to enhance the features without adding any parameters to the original network; Point-NN needs to compute the similarity between each feature at the naive feature similarity matching stage; however, the magnitude difference of the features in vector space during the feature extraction stage may affect the final matching result. We use the Squash operation to squeeze the features. This nonlinear operation can make the features squeeze to a certain range without changing the original direction in the vector space, thus eliminating the effect of feature magnitude, and we can ultimately better complete the naive feature matching in the vector space. We inserted these modules into the network and build a nonparametric network, Point-Sim, which performs well in 3D classification tasks. Based on this, we extend the lightweight neural network Point-SimP by adding some trainable parameters for the point cloud classification task, which requires only 0.8 M parameters for high performance analysis. Experimental results demonstrate the effectiveness of our proposed algorithm in the point cloud shape classification task. The corresponding results on ModelNet40 and ScanObjectNN are 83.9% and 66.3% for 0 M parameters—without any training—and 93.3% and 86.6% for 0.8 M parameters. The Point-SimP reaches a test speed of 962 samples per second on the ModelNet40 dataset. The experimental results show that our proposed method effectively improves the performance on point cloud classification networks.