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Global and Local Structure Preservation for Nonlinear High-dimensional Spectral Clustering
The Computer Journal ( IF 1.5 ) Pub Date : 2021-03-05 , DOI: 10.1093/comjnl/bxab020
Guoqiu Wen 1 , Yonghua Zhu 1 , Linjun Chen 1 , Mengmeng Zhan 1 , Yangcai Xie 2
Affiliation  

Spectral clustering is widely applied in real applications, as it utilizes a graph matrix to consider the similarity relationship of subjects. The quality of graph structure is usually important to the robustness of the clustering task. However, existing spectral clustering methods consider either the local structure or the global structure, which can not provide comprehensive information for clustering tasks. Moreover, previous clustering methods only consider the simple similarity relationship, which may not output the optimal clustering performance. To solve these problems, we propose a novel clustering method considering both the local structure and the global structure for conducting nonlinear clustering. Specifically, our proposed method simultaneously considers (i) preserving the local structure and the global structure of subjects to provide comprehensive information for clustering tasks, (ii) exploring the nonlinear similarity relationship to capture the complex and inherent correlation of subjects and (iii) embedding dimensionality reduction techniques and a low-rank constraint in the framework of adaptive graph learning to reduce clustering biases. These constraints are considered in a unified optimization framework to result in one-step clustering. Experimental results on real data sets demonstrate that our method achieved competitive clustering performance in comparison with state-of-the-art clustering methods.

中文翻译:

非线性高维谱聚类的全局和局部结构保留

光谱聚类在实际应用中得到了广泛的应用,因为它利用图矩阵来考虑对象的相似性关系。图结构的质量通常对聚类任务的鲁棒性很重要。然而,现有的谱聚类方法要么考虑局部结构,要么考虑全局结构,不能为聚类任务提供全面的信息。而且,以往的聚类方法只考虑简单的相似关系,可能无法输出最优的聚类性能。为了解决这些问题,我们提出了一种同时考虑局部结构和全局结构的聚类方法,用于进行非线性聚类。具体来说,我们提出的方法同时考虑(i)保留主体的局部结构和全局结构,为聚类任务提供全面的信息,(ii)探索非线性相似关系以捕捉主体的复杂和内在相关性,以及(iii)嵌入降维自适应图学习框架中的技术和低秩约束以减少聚类偏差。这些约束被考虑在一个统一的优化框架中,以产生一步聚类。真实数据集的实验结果表明,与最先进的聚类方法相比,我们的方法实现了具有竞争力的聚类性能。(ii) 探索非线性相似关系以捕捉对象的复杂和内在相关性,以及 (iii) 在自适应图学习框架中嵌入降维技术和低秩约束以减少聚类偏差。这些约束被考虑在一个统一的优化框架中,以产生一步聚类。真实数据集的实验结果表明,与最先进的聚类方法相比,我们的方法实现了具有竞争力的聚类性能。(ii) 探索非线性相似关系以捕捉对象的复杂和内在相关性,以及 (iii) 在自适应图学习框架中嵌入降维技术和低秩约束以减少聚类偏差。这些约束被考虑在一个统一的优化框架中,以产生一步聚类。真实数据集的实验结果表明,与最先进的聚类方法相比,我们的方法实现了具有竞争力的聚类性能。
更新日期:2021-03-05
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