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高维数据的聚类方法研究与应用
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摘要
聚类分析是数据挖掘中重要的研究课题,在信息过滤、资料自动分类、生物信息学等领域得到广泛应用。随着技术进步,聚类分析许多应用领域的数据具有很高的维度,例如,各种类型的文档数据、基因表达数据等其维度(属性)可以达到成百上千维,甚至更高。由于高维数据存在的普遍性,高维数据的聚类分析具有非常重要的意义。
     数据在高维空间中的表现相对于低维空间有很大的差异。在高维空间的许多情况下,由于数据分布的内在稀疏性,低维数据聚类常用的L_p距离等相似度度量有效性大大降低;高维空间中簇类往往只存在于某些低维子空间中,而不同的簇类其所处的子空间也可能存在差异。受“维度效应”的影响,许多在低维数据上表现良好的聚类方法运用于高维数据时无法获得很好的效果,需要采用一些特殊的方法进行高维数据的聚类分析。
     本文从高维数据子空间聚类的数学统计模型入手,研究其潜在的概率统计模型,继而提出新的聚类算法、开展高维数据的聚类有效性等研究;并在文本分类、网络入侵检测和恶意软件鉴别中进行应用研究,具有一定的理论意义和实际应用价值。
     本文的主要工作及贡献如下:
     1.提出了一种高维数据子空间聚类的概率统计模型及其学习算法,分析了子空间聚类算法的目标优化函数;
     2.建立了现有软子空间聚类算法与统计模型之间的联系,对其中两种代表性算法进行了多方面的改进;提出检测局部离群点的方法,提高了子空间聚类算法的鲁棒性:
     3.基于统计模型给出了模糊隶属度的新定义,提出一种高维数据的模糊聚类算法;结合三种改进的子空间聚类有效性指标,用于估计高维数据集的子空间簇类数目;
     4.针对传统方法需要对大型、高维数据集进行反复聚类引起的计算效率问题,提出了基于层次划分的最佳聚类数目确定方法;
     5.将子空间聚类方法应用于有指导的文本分类,提出了一种具有线性时间复杂度的文本分类新算法:将以上高维数据的聚类方法应用于网络入侵检测系统的关键特征选择和实际项目进行恶意软件辅助鉴别。
Clustering analysis is an important research in data mining, and has been widely used in many fields, such as message filtering, document categorization, bioinformatics, etc. In those fields, the data are always of high dimensions. For examples, the document data and gene microarray data are generated in several hundreds or even a thousand attributes (or dimensions). The universality of these data makes researches on high dimensional data clustering more and more important.
     The characteristics of data objects in high dimensional space are quite different from which in low dimensional space. In many cases, the effectiveness of similarity measurement which is usually adopted in low-dimensional data clustering, such as L_p-norm, will degrade rapidly in high dimensional space, due to the inherent sparsity of the data. In addition, clusters usually only exist in some low-dimensional subspaces, moreover, the subspaces may spanned by different combinations of dimensions within high dimensional data. Due to the curse of high dimensionality, many methods which work well on low-dimensional data will yield poor performances when clustering high dimensional data.
     In order to address these problems, some new methods are proposed in this thesis, which focuses on the issues of new subspace clustering algorithms and high dimensional cluster validition, based on subspace cluster modeling. The methods mentioned above are also used in text categorization, network intrusion detection and malware detection. The researches in this dissertation have much important theoretical and practical significance.
     The majority of our contributions can be summarized as follows:
     1. A probability model for describing the subspace clusters in high dimensional space as well as its learning algorithm and clustering objective function is presented.
     2. Some recent soft subspace clustering algorithms are improved in terms of stability and clustering accuracy, by analyzing their relationships with the probability model. The algorithms are further improved in terms of robustness by embed local outliers detection.
     3. A new definition of the fuzzy membership has been derived based on the probability model, and a fuzzy algorithm for subspace clustering on high dimensional data is proposed. Furthermore, three traditional cluster validity indices are improved to meet with the requirements of subspace clustering. Combing with the fuzzy algorithm, the new subspace cluster validity indices are used to estimate the number of subspace clusters in high dimensional data.
     4. A hierarchical method is presented to estimate the number of clusters on large and high dimensional datasets. The problem of inefficiency, arose by repeatly clustering on large datasets in the traditional approach, is solved in the new method.
     5. A new classification algorithm with linear time complexity is presented for text categorization, by combining unsupervised subspace clustering methods and supervised classification ones. We apply the proposed methods to network intrusion detection for supervised feature selection and a practical project for malware aided detection.
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