Active constraint spectral clustering based on Hessian matrix

Applying the pairwise constraint algorithm to spectral clustering has become a hot topic in data mining research in recent years. In this paper, a clustering algorithm is proposed, called an active constraint spectral clustering based on Hessian matrix (ACSCHM); this algorithm not only use Hessian matrix instead of Laplacian matrix to free the parameter but also use an active query function to dynamically select constraint pairs and use these constraints to tune and optimize data points. In this paper, we used active query strategy to replace the previous random query strategy, which overcame the instability of the clustering results brought by the random query and enhanced the robustness of the algorithm. The unique parameter in the Hessian matrix was obtained by the spectral radius of the matrix, and the parameter selection problem in the original spectral clustering algorithm was also solved. Experiments on multiple UCI data sets can prove the effectiveness of this algorithm.