A Spectral Clustering Algorithm for Similar Matrix Reconstruction based on Adaptive Neighborhood Standard Deviation

In view of the shortcomings of the classical spectral clustering algorithm in the artificial setting of scale parameters and the accuracy of the similar matrix construction, which leads to the low accuracy of the clustering results, a similar matrix reconstruction spectral clustering algorithm based on adaptive neighborhood standard deviation is proposed. The algorithm uses the inverse of the sample neighborhood standard deviation as a parameter to measure the local density of the sample. It constructs an adaptive scale parameter by incorporating a multi-region density adjustment strategy. Additionally, a nonlinear Sigmoid function is introduced to design the scale difference adjustment term, and the similarity matrix is reconstructed by integrating global density. The experimental results demonstrate that the proposed algorithm achieves good clustering performance on both synthetic datasets and real UCI datasets, with more stable clustering results.