高维数据子空间聚类分析及应用研究

发布时间：2021-05-19 23:14

　　聚类是一种重要的数据分析手段。通过聚类分析,人们能有效地发现隐含在数据集中的数据分布特性,从而为进一步充分、有效地利用数据奠定良好的基础。随着信息技术的迅猛发展,聚类所面临的不仅是数据量越来越大的问题,更重要的还是数据的高维度问题。但是,受“维度效应”的影响,许多在低维数据空间表现良好的聚类方法运用在高维空间上往往无法获得好的聚类效果,这对高维数据聚类分析技术提出了很大的挑战。高维数据聚类是聚类分析技术的重点和难点,基于谱聚类的子空间聚类方法是实现高维数据聚类的有效途径。子空间聚类的目的是将来自不同子空间的高维数据分割到本质上所属的低维子空间,它是高维数据聚类的一种新方法,在机器学习、计算机视觉、图像处理和系统辨识等领域有广泛的应用。本文针对高维数据的子空间聚类问题给出了 一些新的聚类模型,主要工作包括以下几个方面:1、通过分析自表示系数矩阵与聚类指标矩阵之间的关系,我们提出了一个新的相似度学习和子空间聚类的统一极小化框架——基于Direction-Grouping-Effect-Within-Cluster的结构稀疏子空间聚类（SSDG）。在SSDG中,为了让本质上属于同一子空间的数... 

【文章来源】：西安电子科技大学陕西省 211工程院校 教育部直属院校

【文章页数】：126 页

【学位级别】：博士

【文章目录】：
ABSTRACT
摘要
List of Symbols
List of Abbreviations
Chapter 1 Introduction
    1.1 Background and significance of the research
    1.2 Introduction to concepts and technologies related to clustering algorithms
        1.2.1 The conventional clustering algorithm
        1.2.2 The subspace clustering
    1.3 Notations
    1.4 The main contributions of the dissertation
Chapter 2 Structured Sparse Subspace Clustering with Direction-Grouping-Effect-Within-Cluster
    2.1 Introduction
    2.2 Related work
    2.3 A unified optimization framework for Structured Sparse Subspace Cluster-ing with DGEWC
    2.4 An alternating minimization algorithm for our model
        2.4.1 Solution of the representation coefficient
        2.4.2 Spectral clustering
        2.4.3 Summary of the proposed algorithm
    2.5 Experiments
        2.5.1 Experiments on Extended Yale B dataset
        2.5.2 Experiments on COIL20 dataset
        2.5.3 Experiments on USPS dataset
        2.5.4 Experiments on ORL dataset
        2.5.5 Experiments on Hopkins 155 dataset
        2.5.6 Runtime costs
        2.5.7 Convergence analysis
    2.6 Conclusion
Chapter 3 Discriminative and Coherent Subspace Clustering
    3.1 Introduction
    3.2 Discriminative and Coherent Subspace Clustering
        3.2.1 Motivation
        3.2.2 DCSC model
        3.2.3 Minimization algorithm
        3.2.4 Connections and differences between DCSC and other related methods
        3.2.5 Summary of the proposed algorithm
    3.3 Experiments
        3.3.1 Experiments on Extended Yale B dataset
        3.3.2 Experiments on the USPS dataset
        3.3.3 Experiments on the Hopkins 155 dataset
        3.3.4 Convergence analysis
    3.4 Conclusion
Chapter 4 Discrimination Enhanced Spectral Clustering
    4.1 Introduction
    4.2 Related work
    4.3 Discrimination Enhanced Spectral Clustering
        4.3.1 Motivation
        4.3.2 DESC model
    4.4 Minimization algorithm
        4.4.1 Weighted sparse spectral clustering
        4.4.2 Solution of the representation coefficient
        4.4.3 Summary of the proposed algorithm
    4.5 Experiments
        4.5.1 Experiments on Extended Yale B dataset
        4.5.2 Experiments on the USPS dataset
        4.5.3 Convergence analysis
    4.6 Conclusion
Chapter 5 Block Diagonal Spectral Clustering
    5.1 Introduction
    5.2 Related work
    5.3 Block Diagonal Spectral Clustering
    5.4 Minimization algorithm
        5.4.1 Minimization algorithm of BDSpeCl
        5.4.2 Minimization algorithm of BDSpeC2
    5.5 Experiments
        5.5.1 Experiments on the Hopkins 155 dataset
        5.5.2 Experiments on the MNIST dataset, USPS dataset and PIE dataset
        5.5.3 Convergence analysis
    5.6 Conclusion
Chapter 6 Conclusions and Future Work
References
Acknowledgements
Curriculum Vitae


【参考文献】：
期刊论文
[1]FDBSCAN:一种快速 DBSCAN算法（英文）[J]. 周水庚,周傲英,金文,范晔,钱卫宁.  软件学报. 2000(06)



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