Low Rank Representation Subspace Clustering Algorithm Based on Hessian Regularization and Non Negative Constraints

Abstract

Existing low rank representation methods do not fully utilize the local structural features of data, resulting in problems such as loss of local similarity during the learning process. This paper proposed to use the low rank representation subspace clustering algorithm based on Hessian regularization and non-negative constraint (LRR-HN), to explore the overall and local structures of data. Firstly, the high predictability of Hessian regularization was fully utilized to preserve the local manifold structure of the data, thereby improving the description of the local topological structure of the data. Secondly, in view of the fact that the obtained coefficient matrix is often positive or negative, and negative values often have no practical significance, this article intended to introduce non negative constraints to ensure the correctness of the model solution and better characterize the local structure of the data. The NMI (Normalized Mutual Information) of Ncut (Normalized cut, Ncut) was 23.3%, and the AC (Accuracy) was 34.6%. The NMI of PCA (Principal Component Analysis) was 25.9%, and the AC was 45.3%. The NMI of LRR-HN was 89.9%, and AC was 93.2%. Experimental results showed that LRR-HN outperformed existing algorithms in areas such as AC and NMI, and had good clustering performance.