图谱聚类的等价模型研究
Research on Equivalent Model of Graph Clustering
DOI: 10.12677/AAM.2023.123129, PDF,   
作者: 刘 昊：重庆理工大学理学院，重庆
关键词: 谱聚类；N-Cut；相似矩阵；图论；Spectral Clustering； N-Cut； Similarity Matrix； Graph Theory
摘要: 聚类分析作为一类非监督学习方法，能够有效挖掘数据中的各类潜在关系。图谱聚类是一种基于相似矩阵的聚类算法，一般转化为无向图的划分问题。为扩展图谱聚类在大数据分析中的应用性，从拉普拉斯矩阵出发，结合邻接矩阵与度矩阵的特点，对图谱聚类的目标函数进行松弛，得到了一类更一般形式的图谱聚类模型。此外，还从理论上证明了松弛后的模型与原问题的等价性及其迭代点列的收敛性。
Abstract: As an unsupervised learning method, clustering analysis can effectively mine various potential re-lationships in data. Graph clustering is a clustering algorithm based on similarity matrix, which is generally transformed into the problem of undirected graph partition. In order to expand the ap-plication of atlas clustering in big data analysis, starting from Laplace matrix, combining the char-acteristics of adjacency matrix and degree matrix, the objective function of atlas clustering is re-laxed, and a more general form of atlas clustering model is obtained. In addition, the equivalence between the relaxed model and the original problem and the convergence of the iterative point se-quence are proved theoretically.
文章引用：刘昊. 图谱聚类的等价模型研究[J]. 应用数学进展, 2023, 12(3): 1273-1280. https://doi.org/10.12677/AAM.2023.123129

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