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.

Chunzhong Li. Low Rank Representation Subspace Clustering Algorithm Based on Hessian Regularization and Non Negative Constraints. International Journal of Social Sciences and Economic Management (2024), Vol. 5, Issue 1: 23-31. https://doi.org/10.38007/IJSSEM.2024.050104.

[1] Liu Yunxiang, Wang Yibin. Adaptive weighted multi view subspace clustering algorithm based on latent representation. Computer Knowledge and Technology: Academic Edition, 2023, 19 (17): 10-15.

[2] Li Huan, Tang Kewei. Multi view subspace clustering based on low rank tensor representation. Theoretical Mathematics, 2023, 13 (10): 2877-2887.

[3] Tu Zhihui, Chen Long, Zhang Zichang, et al. Subspace clustering algorithm for joint Capped norm minimization. Journal of Gannan Normal University, 2020, 041 (006): 56-61.

[4] Yan Jintao, Li Zhongyu, Tang Qifan, et al. Deep low rank multi view subspace clustering. Journal of Xi'an Jiaotong University, 2021, 055 (011): 125-135.

[5] Li Li, Li Jinghao, Zhang Xiaoqian. Potential Multi View Subspace Clustering Based on Tensor Learning. Journal of Southwest University of Science and Technology, 2022, 37 (3): 52-59.

[6] Chen J, Yang S, Mao H, et al. Multiview subspace clustering using low-rank representation. IEEE Transactions on Cybernetics, 2021, 52(11): 12364-12378.

[7] Abhadiomhen S E, Wang Z Y, Shen X J. Coupled low rank representation and subspace clustering. Applied Intelligence, 2022, 52(1): 530-546.

[8] Abhadiomhen S E, Wang Z, Shen X, et al. Multiview common subspace clustering via coupled low rank representation. ACM Transactions on Intelligent Systems and Technology (TIST), 2021, 12(4): 1-25.

[9] Nie F, Chang W, Hu Z, et al. Robust subspace clustering with low-rank structure constraint. IEEE Transactions on Knowledge and Data Engineering, 2020, 34(3): 1404-1415.

[10] Khan G A, Hu J, Li T, et al. Multi-view subspace clustering for learning joint representation via low-rank sparse representation. Applied Intelligence, 2023, 53(19): 22511-22530.

[11] Chen Y, Xiao X, Peng C, et al. Low-rank tensor graph learning for multi-view subspace clustering. IEEE Transactions on Circuits and Systems for Video Technology, 2021, 32(1): 92-104.

[12] Guo J, Sun Y, Gao J, et al. Rank consistency induced multiview subspace clustering via low-rank matrix factorization. IEEE Transactions on Neural Networks and Learning Systems, 2021, 33(7): 3157-3170.

[13] Sun W, Peng J, Yang G, et al. Fast and latent low-rank subspace clustering for hyperspectral band selection. IEEE Transactions on Geoscience and Remote Sensing, 2020, 58(6): 3906-3915.

[14] Peng X, Feng J, Zhou J T, et al. Deep subspace clustering. IEEE transactions on neural networks and learning systems, 2020, 31(12): 5509-5521.

[15] Sui J, Liu Z, Liu L, et al. Dynamic sparse subspace clustering for evolving high-dimensional data streams. IEEE Transactions on Cybernetics, 2020, 52(6): 4173-4186.