一种基于逆近邻和影响空间的DBSCAN聚类分析算法

密度聚类是数据挖掘和机器学习中最常用的分析方法之一,无须预先指定聚类数目就能够发现非球形聚类簇,但存在无法识别不同密度的相邻聚类簇等问题。采用逆近邻和影响空间的思想,提出一种密度聚类分析算法。利用欧氏距离计算数据对象的K近邻与逆近邻,依据逆近邻识别其核心对象,并确定其核心对象的影响空间;利用逆近邻和影响空间,重新定义密度聚类簇扩展条件,并通过广度优先遍历搜索核心对象的影响空间,形成密度聚类簇,有效解决了无法区分不同密度相邻聚类簇等不足,提高了密度聚类分析效果和效率。基于UCI和人工数据集实验验证了该算法的有效性。     

基于密度峰和划分的快速聚类算法

传统基于划分的聚类算法需要人工给定聚类数,且由于算法采取刚性划分,可能会导致将较大或延伸状的聚类簇分割的现象,导致错误的聚类结果。密度峰聚类是近年提出的一种新的基于密度的聚类算法,该算法不需要预先指定聚类数目,且能够发现非球形簇。将密度峰思想引入基于划分的聚类算法,提出一种基于密度峰和划分的快速聚类算法（DDBSCAN）,该算法首先获取一组簇的核心对象(密度峰),用于描述簇的“骨骼”,而后将周围的点划分到最近的核心对象,最后通过判断划分边界处的密度情况合并簇。实验证明,该算法能有效地适应任意形状、大小不一的数据集,与传统基于密度的聚类算法相比收敛速度更快。     

优化子空间的高维聚类算法

针对当前大多数典型软子空间聚类算法未能考虑簇类投影子空间的优化问题,提出一种新的软子空间聚类算法。该算法将最大化权重之间的差异性作为子空间优化的目标,并提出了一个量化公式。以此为基础设计了一个新的优化目标函数,在最小化簇内紧凑度的同时,优化每个簇所在的软子空间。通过数学推导得到了新的特征权重计算方法,并基于k-means算法框架定义了新聚类算法。实验结果表明,所提算法对子空间的优化降低了算法过早陷入局部最优的可能性,提高了算法的稳定性,并且具有良好的性能和聚类效果,适合用于高维数据聚类分析。     

不平衡数据的软子空间聚类算法

针对受均匀效应的影响,当前K-means型软子空间算法不能有效聚类不平衡数据的问题,提出一种基于划分的不平衡数据软子空间聚类新算法。首先,提出一种双加权方法,在赋予每个属性一个特征权重的同时,赋予每个簇反映其重要性的一个簇类权重;其次,提出一种混合型数据的新距离度量,以平衡不同类型属性及具有不同符号数目的类属型属性间的差异;第三,定义了基于双加权方法的不平衡数据子空间聚类目标优化函数,给出了优化簇类权重和特征权重的表达式。在实际应用数据集上进行了系列实验,结果表明,新算法使用的双权重方法能够为不平衡数据中的簇类学习更准确的软子空间;与现有的K-means型软子空间算法相比,所提算法提高了不平衡数据的聚类精度,在其中的生物信息学数据上可以取得近50%的提升幅度。     

自适应的软子空间聚类算法

软子空间聚类是高维数据分析的一种重要手段.现有算法通常需要用户事先设置一些全局的关键参数,且没有考虑子空间的优化.提出了一个新的软子空间聚类优化目标函数,在最小化子空间簇类的簇内紧凑度的同时,最大化每个簇类所在的投影子空间.通过推导得到一种新的局部特征加权方式,以此为基础提出一种自适应的k-means型软子空间聚类算法.该算法在聚类过程中根据数据集及其划分的信息,动态地计算最优的算法参数.在实际应用和合成数据集上的实验结果表明,该算法大幅度提高了聚类精度和聚类结果的稳定性.     

基于混合度量与类簇自适应调整的粗糙模糊K-means聚类算法

针对粗糙K-means聚类及其相关衍生算法需要提前人为给定聚类数目、随机选取初始类簇中心导致类簇交叉区域的数据划分准确率偏低等问题,文中提出基于混合度量与类簇自适应调整的粗糙模糊K-means聚类算法.在计算边界区域的数据对象归属于不同类簇的隶属程度时,综合考虑局部密度和距离的混合度量,并采用自适应调整类簇数目的策略,获得最佳聚类数目.选取数据对象稠密区域中距离最小的两个样本的中点作为初始类簇中心,将附近局部密度高于平均密度的对象划分至该簇后再选取剩余的初始类簇中心,使初始类簇中心的选取更合理.在人工数据集和UCI标准数据集上的实验表明,文中算法在处理类簇交叠严重的球簇状数据集时,具有自适应性,聚类精度较优.     

基于密度与划分方法的聚类算法设计与实现

在分析常用聚类算法的特点和适应性基础上提出一种基于密度与划分方法的聚类算法。该算法根据数据对象密度分布状态来自动确定聚类簇密度吸引中心点和聚类簇的初始划分;然后利用划分的方法,根据密度可达定义来寻找密度可达数据对象簇,从而完成数据对象簇的最终聚类。实验证明该算法能够很好地处理具有任意形状和大小的簇,能够有效地屏蔽噪声和离群点的影响和发现孤立点;同时也减小了输入参数对领域知识的依赖性。     

基于密度网格的数据流聚类算法

针对基于密度网格的数据流聚类算法中存在的缺陷进行改进,提出一种基于D-Strcam算法的改进算法NDD-Stream。算法通过统计网格单元的密度与簇的数目,动态确定网格单元的密度阂值;对位于簇边界的网格单元采用不均匀划分,以提高簇边界的聚类精度。合成与真实数据集上的实验结果表明,算法能够在数据流对象上取得良好的聚类质量。     

一种基于密度和网格的簇心可确定聚类算法

以网格化数据集来减少聚类过程中的计算复杂度,提出一种基于密度和网格的簇心可确定聚类算法.首先网格化数据集空间,以落在单位网格对象里的数据点数表示该网格对象的密度值,以该网格到更高密度网格对象的最近距离作为该网格的距离值;然后根据簇心网格对象同时拥有较高的密度和较大的距离值的特征,确定簇心网格对象,再通过一种基于密度的划分方式完成聚类;最后,在多个数据集上对所提出算法与一些现有聚类算法进行聚类准确性与执行时间的对比实验,验证了所提出算法具有较高的聚类准确性和较快的执行速度.     

基于子空间差异的投影聚类算法

针对传统K-means型软子空间聚类技术中子空间差异度量定义的困难问题,提出一种基于概率距离的子空间差异表示模型,以此为基础提出一种自适应的投影聚类算法。该方法首先基于子空间聚类理论提出一个描述各簇类所关联的软子空间之间的相异度公式;其次,将其与软子空间聚类相结合,定义了聚类目标优化函数,并根据局部搜索策略给出了聚类算法过程。在合成和实际数据集上进行了一系列实验,结果表明该算法引入子空间比较可以为簇类学习更优的软子空间;与现有主流子空间聚类算法相比,所提算法大幅度提升了聚类精度,适用于高维数据聚类分析。     

一种有效的基于网格和密度的聚类分析算法

讨论数据挖掘中聚类的相关概念、技术和算法。提出一种基于网格和密度的算法，它的优点在于能够自动发现包含有趣知识的子空间，并将里面存在的所有聚类挖掘出来；另一方面它能很好地处理高维数据和大数据集的数据表格。算法将最后的结果用DNF的形式表示出来。     

基于Mean-Shift的投影聚类算法PCMF

高维数据的聚类都隐含在低维的子空间内。为找出有效的子空间，Agrawal等人提出了投影聚类概念，通过映射变换转换到子空间里，然后借助其他方法找到聚类。该文基于目前最新的投影聚类算法EPCH，提出了PCMF算法，借助Mean-Shift划分子空间聚类。与EPCH算法相比，PCMF在划分子空间中数据时，无须输入参数（EPCH中是最大聚类个数），能够有效降低划分出的子空间数量，获得与EPCH相媲美的实验结果。     

Algorithm to determine ε-distance parameter in density based clustering

The well known clustering algorithm DBSCAN is founded on the density notion of clustering. However, the use of global density parameter ε-distance makes DBSCAN not suitable in varying density datasets. Also, guessing the value for the same is not straightforward. In this paper, we generalise this algorithm in two ways. First, adaptively determine the key input parameter ε-distance, which makes DBSCAN independent of domain knowledge satisfying the unsupervised notion of clustering. Second, the approach of deriving ε-distance based on checking the data distribution of each dimension makes the approach suitable for subspace clustering, which detects clusters enclosed in various subspaces of high dimensional data. Experimental results illustrate that our approach can efficiently find out the clusters of varying sizes, shapes as well as varying densities.     

高维数据流子空间聚类发现及维护算法

近年来由于数据流应用的大量涌现,基于数据流模型的数据挖掘算法研究已成为重要的应用前沿课题.提出一种基于Hoeffding界的高维数据流的子空间聚类发现及维护算法--SHStream.算法将数据流分段（分段长度由Hoeffding界确定）,在数据分段上进行子空间聚类,通过迭代逐步得到满足聚类精度要求的聚类结果,同时针对数据流的动态性,算法对聚类结果进行调整和维护.算法可以有效地处理高雏数据流和对任意形状分布数据的聚类问题.基于真实数据集与仿真数据集的实验表明,算法具有良好的适用性和有效性.     

A novel soft subspace clustering algorithm with noise detection for high dimensional datasets

When dealing with high dimensional data, clustering faces the curse of dimensionality problem. In such data sets, clusters of objects exist in subspaces rather than in whole feature space. Subspace clustering algorithms have already been introduced to tackle this problem. However, noisy data points present in this type of data can have great impact on the clustering results. Therefore, to overcome these problems simultaneously, the fuzzy soft subspace clustering with noise detection (FSSC-ND) is proposed. The presented algorithm is based on the entropy weighting soft subspace clustering and noise clustering. The FSSC-ND algorithm uses a new objective function and update rules to achieve the mentioned goals and present more interpretable clustering results. Several experiments have been conducted on artificial and UCI benchmark datasets to assess the performance of the proposed algorithm. In addition, a number of cancer gene expression datasets are used to evaluate the performance of the proposed algorithm when dealing with high dimensional data. The results of these experiments demonstrate the superiority of the FSSC-ND algorithm in comparison with the state of the art clustering algorithms developed in earlier research.     

Enhancing subspace clustering based on dynamic prediction

In high dimensional data, many dimensions are irrelevant to each other and clusters are usually hidden under noise. As an important extension of the traditional clustering, subspace clustering can be utilized to simultaneously cluster the high dimensional data into several subspaces and associate the low-dimensional subspaces with the corresponding points. In subspace clustering, it is a crucial step to construct an affinity matrix with block-diagonal form, in which the blocks correspond to different clusters. The distance-based methods and the representation-based methods are two major types of approaches for building an informative affinity matrix. In general, it is the difference between the density inside and outside the blocks that determines the efficiency and accuracy of the clustering. In this work, we introduce a well-known approach in statistic physics method, namely link prediction, to enhance subspace clustering by reinforcing the affinity matrix.More importantly,we introduce the idea to combine complex network theory with machine learning. By revealing the hidden links inside each block, we maximize the density of each block along the diagonal, while restrain the remaining non-blocks in the affinity matrix as sparse as possible. Our method has been shown to have a remarkably improved clustering accuracy comparing with the existing methods on well-known datasets.     

An extended EM algorithm for subspace clustering

Clustering high dimensional data has become a challenge in data mining due to the curse of dimensionality. To solve this problem, subspace clustering has been defined as an extension of traditional clustering that seeks to find clusters in subspaces spanned by different combinations of dimensions within a dataset. This paper presents a new subspace clustering algorithm that calculates the local feature weights automatically in an EM-based clustering process. In the algorithm, the features are locally weighted by using a new unsupervised weighting method, as a means to minimize a proposed clustering criterion that takes into account both the average intra-clusters compactness and the average inter-clusters separation for subspace clustering. For the purposes of capturing accurate subspace information, an additional outlier detection process is presented to identify the possible local outliers of subspace clusters, and is embedded between the E-step and M-step of the algorithm. The method has been evaluated in clustering real-world gene expression data and high dimensional artificial data with outliers, and the experimental results have shown its effectiveness.     

A distance-relatedness dynamic model for clustering high dimensional data of arbitrary shapes and densities

It is important to find the natural clusters in high dimensional data where visualization becomes difficult. A natural cluster is a cluster of any shape and density, and it should not be restricted to a globular shape as a wide number of algorithms assume, or to a specific user-defined density as some density-based algorithms require.In this work, it is proposed to solve the problem by maximizing the relatedness of distances between patterns in the same cluster. It is then possible to distinguish clusters based on their distance-based densities. A novel dynamic model is proposed based on new distance-relatedness measures and clustering criteria. The proposed algorithm “Mitosis” is able to discover clusters of arbitrary shapes and arbitrary densities in high dimensional data. It has a good computational complexity compared to related algorithms. It performs very well on high dimensional data, discovering clusters that cannot be found by known algorithms. It also identifies outliers in the data as a by-product of the cluster formation process. A validity measure that depends on the main clustering criterion is also proposed to tune the algorithm's parameters. The theoretical bases of the algorithm and its steps are presented. Its performance is illustrated by comparing it with related algorithms on several data sets.     

一种高维数据聚类遗传算法

聚类分析是数据挖掘中的一个重要研究课题。在许多实际应用中,聚类分析的数据往往具有很高的维度,例如文档数据、基因微阵列等数据可以达到上千维,而在高维数据空间中,数据的分布较为稀疏。受这些因素的影响,许多对低维数据有效的经典聚类算法对高维数据聚类常常失效。针对这类问题,本文提出了一种基于遗传算法的高维数据聚类新方法。该方法利用遗传算法的全局搜索能力对特征空间进行搜索,以找出有效的聚类特征子空间。同时,为了考察特征维在子空间聚类中的特征,本文设计出一种基于特征维对子空间聚类贡献率的适应度函数。人工数据、真实数据的实验结果以及与k-means算法的对比实验证明了该方法的可行性和有效性。