计算机科学与探索2024，Vol.18Issue(3)：659-673,15.DOI:10.3778/j.issn.1673-9418.2212041
平滑非负低秩图表示聚类算法
Smooth Non-negative Low-Rank Graph Representation for Clustering
摘要
Abstract
The existing low-rank graph representation algorithms fail to capture the global representation structure of data accurately,and cannot make full use of the valid information of data to guide the construction of the repre-sentation graph,then the constructed representation graph does not have a connected structure suitable for cluster-ing.A smooth non-negative low-rank graph representation method for clustering(SNLRR)is proposed to solve these problems.To more accurately capture the global representation structure of data,SNLRR uses a logarithmic determinant function that is more consistent with the rank characteristics of the matrix to replace the kernel norm to estimate the rank function smoothly,which can effectively reduce the impact of larger singular values of the matrix on the rank estimation,balance the contribution of all singular values to the rank estimation,enhance the accuracy of the rank estimation,so as to more accurately capture the global representation structure of the data.The distance regularization term is also introduced to adaptively assign the optimal nearest neighbor learning representation ma-trix for each data point to capture the local representation structure of data.Besides,SNLRR applies rank constraint on the Laplace matrix of representation matrix so that the learned representation graph has the same number of con-nected components as the real number of clusters,that is,the resulting representation graph has a interconnected structure suitable for clustering.Experimental results on seven datasets with high dimensions and complex distribu-tion,using eight comparison algorithms,show that the clustering performance of SNLRR algorithm is better than that of the eight comparison algorithms,with an average increase of 0.2073 in accuracy and 0.1758 in NMI.There-fore,SNLRR is a graph representation clustering algorithm that can effectively handle data with high dimensions and complex distribution.关键词
聚类/低秩表示/秩约束/对数行列式低秩Key words
clustering/low-rank representation/rank constraint/logarithmic determinant low rank分类
信息技术与安全科学引用本文复制引用
钱罗雄,陈梅,张弛,张锦宏,马学艳..平滑非负低秩图表示聚类算法[J].计算机科学与探索,2024,18(3):659-673,15.基金项目
国家自然科学基金(62266029) （62266029）
甘肃省重点研发计划(21YF5GA053) （21YF5GA053）
甘肃省高等学校产业支撑计划项目(2022CYZC-36).This work was supported by the National Natural Science Foundation of China(62266029),the Key Research and Development Pro-gram of Gansu Province(21YF5GA053),and the Industry Support Program of Higher Education of Gansu Province(2022CYZC-36). （2022CYZC-36）
