一种基于密度的空间数据流在线聚类算法

为了解决空间数据流中任意形状簇的聚类问题,提出了一种基于密度的空间数据流在线聚类算法(On-line density-based clustering algorithm for spatial datastream,OLDStream),该算法在先前聚类结果上聚类增量空间数据,仅对新增空间点及其满足核心点条件的邻域数据做局部聚类更新,降低聚类更新的时间复杂度,实现对空间数据流的在线聚类.OLDStream算法具有快速处理大规模空间数据流、实时获取全局任意形状的聚类簇结果、对数据流的输入顺序不敏感、并能发现孤立点数据等优势.在真实数据和合成数据上的综合实验验证了算法的聚类效果、高效率性和较高的可伸缩性,同时实验结果的统计分析显示仅有4%的空间点消耗最坏运行时间,对每个空间点的平均聚类时间约为0.033 ms.     

优化初始聚类中心的K-means聚类算法

针对传统K-means算法对初始中心十分敏感,聚类结果不稳定问题,提出了一种改进K-means聚类算法。该算法首先计算样本间的距离,根据样本距离找出距离最近的两点形成集合,根据点与集合的计算公式找出其他所有离集合最近的点,直到集合内数据数目大于或等于[α]（[α]为样本集数据点数目与聚类的簇类数目的比值）,再把该集合从样本集中删除,重复以上步骤得到K（K为簇类数目）个集合,计算每个集合的均值作为初始中心,并根据K-means算法得到最终的聚类结果。在Wine、Hayes-Roth、Iris、Tae、Heart-stalog、Ionosphere、Haberman数据集中,改进算法比传统K-means、K-means++算法的聚类结果更稳定;在Wine、Iris、Tae数据集中,比最小方差优化初始聚类中心的K-means算法聚类准确率更高,且在7组数据集中改进算法得到的轮廓系数和F1值最大。对于密度差异较大数据集,聚类结果比传统K-means、K-means++算法更稳定,更准确,且比最小方差优化初始聚类中心的K-means算法更高效。     

A k-means type clustering algorithm for subspace clustering of mixed numeric and categorical datasets

Almost all subspace clustering algorithms proposed so far are designed for numeric datasets. In this paper, we present a k-means type clustering algorithm that finds clusters in data subspaces in mixed numeric and categorical datasets. In this method, we compute attributes contribution to different clusters. We propose a new cost function for a k-means type algorithm. One of the advantages of this algorithm is its complexity which is linear with respect to the number of the data points. This algorithm is also useful in describing the cluster formation in terms of attributes contribution to different clusters. The algorithm is tested on various synthetic and real datasets to show its effectiveness. The clustering results are explained by using attributes weights in the clusters. The clustering results are also compared with published results.     

一种基于影响因子的快速K-均值算法

K-均值聚类算法的执行时间过度依赖于初始点的选取，但是在实际问题中并不知道k的取值和怎样才能有效地选取初始点。在对K-均值算法中初始点的选取进行深入研究的基础上，提出了一种有效的初始点选取算法。现存的类间相似度并不能很好地度量两个类的相似性，为此提出了一种新颖的度量方法：类间影响因子，使用类间影响因子对类进行合并。该方法和上面提出的初始点选取算法能够根据数据集本身的特性快速地自动选取初始中心并给出初始点的个数。最后用高斯数据集对算法进行测试，得到了一个令人满意的结果。     

基于聚类准则函数的改进K-means算法

K-means算法所使用的聚类准则函数是将数据集中各个簇的误差平方值直接相加而得到的,不能有效处理簇的密度不均且大小差异较大的数据集。为此,将K-means算法的聚类准则函数定义为加权的簇内标准差之和,权重为簇内数据对象数占总数目的比例。同时,调整了传统K-means算法将数据对象重新分配给簇的方法,采用一个数据对象到中心点的加权距离代替传统K-means算法中的距离,将数据对象分配给使加权距离最小的中心点所在的簇。实验结果表明,针对模拟数据集的聚类,改进K-means算法可以明显减少大而稀的簇中数据对象被错误地分配到相邻的小而密簇的可能性,改善了聚类的质量;针对UCI数据集的聚类,改进算法使得各个簇更为紧凑,从而验证了改进K-means算法的有效性。     

Density-Based Clustering in Spatial Databases: The Algorithm GDBSCAN and Its Applications

The clustering algorithm DBSCAN relies on a density-based notion of clusters and is designed to discover clusters of arbitrary shape as well as to distinguish noise. In this paper, we generalize this algorithm in two important directions. The generalized algorithm—called GDBSCAN—can cluster point objects as well as spatially extended objects according to both, their spatial and their nonspatial attributes. In addition, four applications using 2D points (astronomy), 3D points (biology), 5D points (earth science) and 2D polygons (geography) are presented, demonstrating the applicability of GDBSCAN to real-world problems.     

基于密度的模糊代表点聚类算法

结合密度聚类和模糊聚类的特点,提出一种基于密度的模糊代表点聚类算法.首先利用密度对数据点成为候选聚类中心点的可能性进行处理,密度越高的点成为聚类中心点的可能性越大;然后利用模糊方法对聚类中心点进行确定;最后通过合并聚类中心点确定最终的聚类中心.所提出算法具有很好的自适应性,能够处理不同形状的聚类问题,无需提前规定聚类个数,能够自动确定真实存在的聚类中心点,可解释性好.通过结合不同聚类方法的优点,最终实现对数据的有效划分.此外,所提出的算法对于聚类数和初始化、处理不同形状的聚类问题以及应对异常值等方面具有较好的鲁棒性.通过在人工数据集和UCI真实数据集上进行实验,表明所提出算法具有较好的聚类性能和广泛的适用性.     

快速模糊C均值聚类彩色图像分割方法

模糊C均值(FCM)聚类用于彩色图像分割具有简单直观、易于实现的特点，但存在聚类性能受中心点初始化影响且计算量大等问题，为此，提出了一种快速模糊聚类方法(FFCM)。这种方法利用分层减法聚类把图像数据分成一定数量的色彩相近的子集，一方面，子集中心用于初始化聚类中心点；另一方面，利用子集中心点和分布密度进行模糊聚类，由于聚类样本数量显著减少以及分层减法聚类计算量小，故可以大幅提高模糊C均值算法的计算速度，进而可以利用聚类有效性分析指标快速确定聚类数目。实验表明，这种方法不需事先确定聚类数目并且在优化聚类性能不变的前提下，可以使模糊聚类的速度得到明显提高，实现彩色图像的快速分割。     

Molecular dynamics-like data clustering approach

Based on the molecular kinetic theory, a molecular dynamics-like data clustering approach is proposed in this paper. Clusters are extracted after data points fuse in the iterating space by the dynamical mechanism that is similar to the interacting mechanism between molecules through molecular forces. This approach is to find possible natural clusters without pre-specifying the number of clusters. Compared with 3 other clustering methods (trimmed k-means, JP algorithm and another gravitational model based method), this approach found clusters better than the other 3 methods in the experiments.     

Scalable Clustering Algorithms with Balancing Constraints

Clustering methods for data-mining problems must be extremely scalable. In addition, several data mining applications demand that the clusters obtained be balanced, i.e., of approximately the same size or importance. In this paper, we propose a general framework for scalable, balanced clustering. The data clustering process is broken down into three steps: sampling of a small representative subset of the points, clustering of the sampled data, and populating the initial clusters with the remaining data followed by refinements. First, we show that a simple uniform sampling from the original data is sufficient to get a representative subset with high probability. While the proposed framework allows a large class of algorithms to be used for clustering the sampled set, we focus on some popular parametric algorithms for ease of exposition. We then present algorithms to populate and refine the clusters. The algorithm for populating the clusters is based on a generalization of the stable marriage problem, whereas the refinement algorithm is a constrained iterative relocation scheme. The complexity of the overall method is O(kN log N) for obtaining k balanced clusters from N data points, which compares favorably with other existing techniques for balanced clustering. In addition to providing balancing guarantees, the clustering performance obtained using the proposed framework is comparable to and often better than the corresponding unconstrained solution. Experimental results on several datasets, including high-dimensional (>20,000) ones, are provided to demonstrate the efficacy of the proposed framework.

DBCURE-MR: An efficient density-based clustering algorithm for large data using MapReduce

Clustering is a useful data mining technique which groups data points such that the points within a single group have similar characteristics, while the points in different groups are dissimilar. Density-based clustering algorithms such as DBSCAN and OPTICS are one kind of widely used clustering algorithms. As there is an increasing trend of applications to deal with vast amounts of data, clustering such big data is a challenging problem. Recently, parallelizing clustering algorithms on a large cluster of commodity machines using the MapReduce framework have received a lot of attention.In this paper, we first propose the new density-based clustering algorithm, called DBCURE, which is robust to find clusters with varying densities and suitable for parallelizing the algorithm with MapReduce. We next develop DBCURE-MR, which is a parallelized DBCURE using MapReduce. While traditional density-based algorithms find each cluster one by one, our DBCURE-MR finds several clusters together in parallel. We prove that both DBCURE and DBCURE-MR find the clusters correctly based on the definition of density-based clusters. Our experimental results with various data sets confirm that DBCURE-MR finds clusters efficiently without being sensitive to the clusters with varying densities and scales up well with the MapReduce framework.     

Using Self-Similarity to Cluster Large Data Sets

Clustering is a widely used knowledge discovery technique. It helps uncovering structures in data that were not previously known. The clustering of large data sets has received a lot of attention in recent years, however, clustering is a still a challenging task since many published algorithms fail to do well in scaling with the size of the data set and the number of dimensions that describe the points, or in finding arbitrary shapes of clusters, or dealing effectively with the presence of noise. In this paper, we present a new clustering algorithm, based in self-similarity properties of the data sets. Self-similarity is the property of being invariant with respect to the scale used to look at the data set. While fractals are self-similar at every scale used to look at them, many data sets exhibit self-similarity over a range of scales. Self-similarity can be measured using the fractal dimension. The new algorithm which we call Fractal Clustering (FC) places points incrementally in the cluster for which the change in the fractal dimension after adding the point is the least. This is a very natural way of clustering points, since points in the same cluster have a great degree of self-similarity among them (and much less self-similarity with respect to points in other clusters). FC requires one scan of the data, is suspendable at will, providing the best answer possible at that point, and is incremental. We show via experiments that FC effectively deals with large data sets, high-dimensionality and noise and is capable of recognizing clusters of arbitrary shape.     

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。     

一种基于粒子群优化的可能性C均值聚类改进方法

提出了一种基于拉子群优化的可能性c均值(Possibilistic Gmeans, PCM)聚类改进方法。该方法首先通过 改进PCM算法的目标函数来计算数据模式的隶属度矩阵和聚类中心完成粒子编码,从而降低算法对初始中心的敏 感,提高聚类的精度;其次,通过粒子群优化(Particle Swarm Optimization, PSO)算法对编码进行优化,以有效地克服 PCM聚类算法容易导致聚类一致性和陷入局部最优解的缺点,减少算法的迭代次数。通过人造数据集和UCI数据 集上的实验,表明该算法在计算复杂度、聚类精度和全局寻优能力方面表现得较为突出。     

使用均值距离与关联性标记的并行OPTICS算法

针对大数据环境下传统并行密度聚类算法中存在的数据划分不合理,聚类结果准确度不高,结果受参数影响较大以及并行效率低等问题,提出一种MapReduce下使用均值距离与关联性标记的并行OPTICS算法——POMDRM-MR。算法使用一种基于维度稀疏度的减少边界点划分策略（DS-PRBP）,划分数据集;针对各个分区,提出标记点排序识别簇算法（MOPTICS）,构建数据点与核心点之间的关联性,并标记数据点迭代次数,在距离度量中,使用领域均值距离策略（FMD）,计算数据点的领域均值距离,代替可达距离排序,输出关联性标记序列;最后结合重排序序列提取簇算法（REC）,对输出序列进行二次排序并提取簇,提高算法局部聚类的准确性和稳定性;在合并全局簇时,算法提出边界密度筛选策略（BD-FLC）,计算筛选密度相近局部簇;又基于n叉树的并集型合并与MapReduce模型,提出并行局部簇合并算法（MCNT-MR）,加快局部簇收敛,并行合并局部簇,提升全局簇合并效率。对照实验表明,POMDRM-MR算法聚类效果更佳,且在大规模数据集下算法的并行化性能更好。     

基于网格和最近邻居的聚类算法

针对目前已有的聚类算法不能很好地处理包含不同密度的簇数据,或者不能很好地区分相邻的密度相差不大的簇的问题,提出1种新的基于严格最近邻居和共享最近邻居的聚类算法．通过构造共享严格最近邻图,使样本点在密度一致的区域保持连接,而在密度不同的相邻区域断开连接,并尽可能去除噪声点和孤立点．该算法可以处理包含有不同密度的簇数据,而且在处理高维数据时具有较低的时间复杂度、实验结果证明,该算法能有效找出不同大小、形状和密度的聚类．     

基于密度梯度的聚类算法研究

针对聚类中不规格形状数据点分布的处理难题,提出了一种基于密度梯度的聚类算法（CDG）。算法通过分析数据样本及其周边的点密度变化情况,选择沿密度变化大的方向寻找不动点,从而获取原始聚类中心,再利用类间边界点的分布情况对小类进行合并。实验结果表明,新算法较基于密度的带噪声数据应用的空间聚类方法（DBSCAN）具有更好的聚类性能。     

基于蛋白质相互作用网络图的聚类方法

依据人类AD（Alzheimer’s Disease）相关蛋白质相互作用网络图,利用基于算术平均最小值——AAMV（Arithmetic Average Minimum Value）的K-means聚类方法对蛋白质进行聚类并预测4个孤立蛋白质的功能。分析结果表明：所得结果与用Maryland Bridge 法及Korbel法所得结果非常相似。     

高维数据流的自适应子空间聚类算法

高维数据流聚类是数据挖掘领域中的研究热点。由于数据流具有数据量大、快速变化、高维性等特点,许多聚类算法不能取得较好的聚类质量。提出了高维数据流的自适应子空间聚类算法SAStream。该算法改进了HPStream中的微簇结构并定义了候选簇,只在相应的子空间内计算新来数据点到候选簇质心的距离,减少了聚类时被检查微簇的数目,将形成的微簇存储在金字塔时间框架中,使用时间衰减函数删除过期的微簇;当数据流量大时,根据监测的系统资源使用情况自动调整界限半径和簇选择因子,从而调节聚类的粒度。实验结果表明,该算法具有良好的聚类质量和快速的数据处理能力。     

多代表点特征树与空间聚类算法

空间数据具有海量、复杂、连续、空间自相关、存在缺损与误差等的特点，要求空间聚类算法具有高效率，能处理各种复杂形状的簇，聚类结果与数据空间分布顺序无关，并且对离群点是健壮的等性能，已有的算法难以同时满足要求。本文提出了一个适合处理海量复杂空间数据的数据结构一多代表点特征树。基于多代表点特征树提出了适合挖掘海量复杂空间数据聚类算法CAMFT，该算法利用多代表点特征树对海量的数据进行压缩，结合随机采样的方法进一步增强算法处理海量数据的能力；同时，多代表点特征树能够保存复杂形状的聚类特征，适合处理复杂空间数据。实验表明了算法CAMFT能够快速处理带有离群点的复杂形状聚类的空间数据，结果与对象空间分布顺序无关，并且效率优于已有的同类聚类算法BLRCH与CURE。