MultiClusterTree: Interactive Visual Exploration of Hierarchical Clusters in Multidimensional Multivariate Data

Visual analytics of multidimensional multivariate data is a challenging task because of the difficulty in understanding metrics in attribute spaces with more than three dimensions. Frequently, the analysis goal is not to look into individual records but to understand the distribution of the records at large and to find clusters of records with similar attribute values. A large number of (typically hierarchical) clustering algorithms have been developed to group individual records to clusters of statistical significance. However, only few visualization techniques exist for further exploring and understanding the clustering results. We propose visualization and interaction methods for analyzing individual clusters as well as cluster distribution within and across levels in the cluster hierarchy. We also provide a clustering method that operates on density rather than individual records. To not restrict our search for clusters, we compute density in the given multidimensional multivariate space. Clusters are formed by areas of high density. We present an approach that automatically computes a hierarchical tree of high density clusters. To visually represent the cluster hierarchy, we present a 2D radial layout that supports an intuitive understanding of the distribution structure of the multidimensional multivariate data set. Individual clusters can be explored interactively using parallel coordinates when being selected in the cluster tree. Furthermore, we integrate circular parallel coordinates into the radial hierarchical cluster tree layout, which allows for the analysis of the overall cluster distribution. This visual representation supports the comprehension of the relations between clusters and the original attributes. The combination of the 2D radial layout and the circular parallel coordinates is used to overcome the overplotting problem of parallel coordinates when looking into data sets with many records. We apply an automatic coloring scheme based on the 2D radial layout of the hierarchical cluster tree encoding hue, saturation, and value of the HSV color space. The colors support linking the 2D radial layout to other views such as the standard parallel coordinates or, in case data is obtained from multidimensional spatial data, the distribution in object space.     

Interactive Visual Analysis of Temporal Cluster Structures

Cluster analysis is a useful method which reveals underlying structures and relations of items after grouping them into clusters. In the case of temporal data, clusters are defined over time intervals where they usually exhibit structural changes. Conventional cluster analysis does not provide sufficient methods to analyze these structural changes, which are, however, crucial in the interpretation and evaluation of temporal clusters. In this paper, we present two novel and interactive visualization techniques that enable users to explore and interpret the structural changes of temporal clusters. We introduce the temporal cluster view, which visualizes the structural quality of a number of temporal clusters, and temporal signatures, which represents the structure of clusters over time. We discuss how these views are utilized to understand the temporal evolution of clusters. We evaluate the proposed techniques in the cluster analysis of mixed lipid bilayers.     

基于改进K-medoids的聚类质量评价指标研究

为了更好地评价无监督聚类算法的聚类质量,解决因簇中心重叠而导致的聚类评价结果失效等问题,对常用聚类评价指标进行了分析,提出一个新的内部评价指标,将簇间邻近边界点的最小距离平方和与簇内样本个数的乘积作为整个样本集的分离度,平衡了簇间分离度与簇内紧致度的关系;提出一种新的密度计算方法,将样本集与各样本的平均距离比值较大的对象作为高密度点,使用最大乘积法选取相对分散且具有较高密度的数据对象作为初始聚类中心,增强了K-medoids算法初始中心点的代表性和算法的稳定性,在此基础上,结合新提出的内部评价指标设计了聚类质量评价模型,在UCI和KDD CUP 99数据集上的实验结果表明,新模型能够对无先验知识样本进行有效聚类和合理评价,能够给出最优聚类数目或最优聚类范围.     

Permutation-test-based clustering method for detection of dynamic patterns in Spatio-temporal datasets

Massive spatio-temporal data have been collected from the earth observation systems for monitoring the changes of natural resources and environment. To find the interesting dynamic patterns embedded in spatio-temporal data, there is an urgent need for detecting spatio-temporal clusters formed by objects with similar attribute values occurring together across space and time. Among different clustering methods, the density-based methods are widely used to detect such spatio-temporal clusters because they are effective for finding arbitrarily shaped clusters and rely on less priori knowledge (e.g. the cluster number). However, a series of user-specified parameters is required to identify high-density objects and to determine cluster significance. In practice, it is difficult for users to determine the optimal clustering parameters; therefore, existing density-based clustering methods typically exhibit unstable performance. To overcome these limitations, a novel density-based spatio-temporal clustering method based on permutation tests is developed in this paper. High-density objects and cluster significance are determined based on statistical information on the dataset. First, the density of each object is defined based on the local variance and a fast permutation test is conducted to identify high-density objects. Then, a proposed two-stage grouping strategy is implemented to group high-density objects and their neighbors; hence, spatio-temporal clusters are formed by minimizing the inhomogeneity increase. Finally, another newly developed permutation test is conducted to evaluate the cluster significance based on the cluster member permutation. Experiments on both simulated and meteorological datasets show that the proposed method exhibits superior performance to two state-of-the-art clustering methods, i.e., ST-DBSCAN and ST-OPTICS. The proposed method can not only identify inherent cluster patterns in spatio-temporal datasets, but also greatly alleviates the difficulty in selecting appropriate clustering parameters.     

A shrinking-based clustering approach for multidimensional data

Existing data analysis techniques have difficulty in handling multidimensional data. Multidimensional data has been a challenge for data analysis because of the inherent sparsity of the points. In this paper, we first present a novel data preprocessing technique called shrinking which optimizes the inherent characteristic of distribution of data. This data reorganization concept can be applied in many fields such as pattern recognition, data clustering, and signal processing. Then, as an important application of the data shrinking preprocessing, we propose a shrinking-based approach for multidimensional data analysis which consists of three steps: data shrinking, cluster detection, and cluster evaluation and selection. The process of data shrinking moves data points along the direction of the density gradient, thus generating condensed, widely-separated clusters. Following data shrinking, clusters are detected by finding the connected components of dense cells (and evaluated by their compactness). The data-shrinking and cluster-detection steps are conducted on a sequence of grids with different cell sizes. The clusters detected at these scales are compared by a cluster-wise evaluation measurement, and the best clusters are selected as the final result. The experimental results show that this approach can effectively and efficiently detect clusters in both low and high-dimensional spaces.     

Model-Based Clustering and Visualization of Navigation Patterns on a Web Site

We present a new methodology for exploring and analyzing navigation patterns on a web site. The patterns that can be analyzed consist of sequences of URL categories traversed by users. In our approach, we first partition site users into clusters such that users with similar navigation paths through the site are placed into the same cluster. Then, for each cluster, we display these paths for users within that cluster. The clustering approach we employ is model-based (as opposed to distance-based) and partitions users according to the order in which they request web pages. In particular, we cluster users by learning a mixture of first-order Markov models using the Expectation-Maximization algorithm. The runtime of our algorithm scales linearly with the number of clusters and with the size of the data; and our implementation easily handles hundreds of thousands of user sessions in memory. In the paper, we describe the details of our method and a visualization tool based on it called WebCANVAS. We illustrate the use of our approach on user-traffic data from msnbc.com.     

Model-based multidimensional clustering of categorical data

Existing models for cluster analysis typically consist of a number of attributes that describe the objects to be partitioned and one single latent variable that represents the clusters to be identified. When one analyzes data using such a model, one is looking for one way to cluster data that is jointly defined by all the attributes. In other words, one performs unidimensional clustering. This is not always appropriate. For complex data with many attributes, it is more reasonable to consider multidimensional clustering, i.e., to partition data along multiple dimensions. In this paper, we present a method for performing multidimensional clustering on categorical data and show its superiority over unidimensional clustering.     

A SOM prototype-based cluster analysis methodology

Data clustering is aimed at finding groups of data that share common hidden properties. These kinds of techniques are especially critical at early stages of data analysis where no information about the dataset is available. One of the mayor shortcomings of the clustering algorithms is the difficulty for non-experts users to configure them and, in some cases, interpret the results. In this work a computational approach with a two-layer structure based on Self-Organizing Map (SOM) is presented for cluster analysis. In the first level, a quantization of the data samples using topology-preserving metrics to automatically determine the number of units in the SOM is proposed. In the second level the obtained SOM prototypes are clustered by means of a connectivity analysis to explore the quality of the partitioning with different number of clusters. The most important benefit of this two-layer procedure is that computational load decreases considerably in comparison with data based clustering methods, making it possible to cluster large data sets and to consider several different clustering alternatives in a limited time. This methodology produces a two-dimensional map representation of the, usually, high dimensional input space, along with quantitative information on viable clustering alternatives, which facilitates the exploration of the possible partitions in a dataset. The efficiency and interpretation of the methodology is illustrated by its application to artificial, benchmark and real complex biological datasets. The experimental results demonstrate the ability of the method to identify possible segmentations in a dataset, compared to algorithms that only yield a single clustering solution. The proposed algorithm tackles the intrinsic limitations of SOM and the parameter settings associated with the clustering methodology, without requiring the number of clusters or the SOM architecture as a prerequisite, among others. This way, it makes possible its application even by researchers with a limited expertise in machine learning.     

On cluster tree for nested and multi-density data clustering

Clustering is one of the important data mining tasks. Nested clusters or clusters of multi-density are very prevalent in data sets. In this paper, we develop a hierarchical clustering approach—a cluster tree to determine such cluster structure and understand hidden information present in data sets of nested clusters or clusters of multi-density. We embed the agglomerative k-means algorithm in the generation of cluster tree to detect such clusters. Experimental results on both synthetic data sets and real data sets are presented to illustrate the effectiveness of the proposed method. Compared with some existing clustering algorithms (DBSCAN, X-means, BIRCH, CURE, NBC, OPTICS, Neural Gas, Tree-SOM, EnDBSAN and LDBSCAN), our proposed cluster tree approach performs better than these methods.     

平行坐标轴动态排列的地理空间多维数据可视分析

目的 平行坐标是经典的多维数据可视化方法,但在用于地理空间多维数据分析时,往往存在空间位置信息缺失和空间关联分析不确定等问题。对此,本文设计了一种有效关联平行坐标和地图的地理空间多维数据可视分析方法。方法 根据多维属性信息对地理空间位置进行聚类分析,引入Voronoi图和颜色明暗映射对地理空间各类区域进行显著标识,利用平行坐标呈现地理空间多维属性信息,引入互信息度量地理空间聚类与属性类别的相关性,动态地确定平行坐标轴排列顺序,进一步计算属性轴与地图之间数据线的绑定位置,对数据线的布局进行优化处理,降低地图与平行坐标系间数据线分布的紊乱程度。结果 有效集成上述可视化设计及数据分析方法,设计与实现一种基于平行坐标轴动态排列的地理空间多维数据可视化分析系统,提供便捷的用户交互模式,通过2组具有明显地理空间多维属性特征的数据进行测试,验证了本文可视分析方法的有效性和实用性。结论 本文提出的可视分析方法和工具可以帮助用户快速分析地理空间多维属性存在的空间分布特征及其关联模式,为地理空间多维数据的探索提供了有效手段。     

Uncovering Representative Groups in Multidimensional Projections

Multidimensional projection‐based visualization methods typically rely on clustering and attribute selection mechanisms to enable visual analysis of multidimensional data. Clustering is often employed to group similar instances according to their distance in the visual space. However, considering only distances in the visual space may be misleading due to projection errors as well as the lack of guarantees to ensure that distinct clusters contain instances with different content. Identifying clusters made up of a few elements is also an issue for most clustering methods. In this work we propose a novel multidimensional projection‐based visualization technique that relies on representative instances to define clusters in the visual space. Representative instances are selected by a deterministic sampling scheme derived from matrix decomposition, which is sensitive to the variability of data while still been able to handle classes with a small number of instances. Moreover, the sampling mechanism can easily be adapted to select relevant attributes from each cluster. Therefore, our methodology unifies sampling, clustering, and feature selection in a simple framework. A comprehensive set of experiments validate our methodology, showing it outperforms most existing sampling and feature selection techniques. A case study shows the effectiveness of the proposed methodology as a visual data analysis tool.     

A clustering method based on multidimensional texture analysis

Considering the analogy between image segmentation and cluster analysis, the aim of this paper is to adapt statistical texture measures to describe the spatial distribution of multidimensional observations. The main idea is to consider the cluster cores as domains characterized by their specific textures in the data space. The distribution of the data points is first described as a multidimensional histogram defined on a multidimensional regular array of sampling points. In order to evaluate locally a multidimensional texture, a co-occurrence matrix is introduced, which characterizes the local distribution of the data points in the multidimensional data space. Several local texture features can be computed from this co-occurrence matrix, which accumulates spatial and statistical information on the data distribution in the neighborhoods of the sampling points. Texture features are selected according to their ability to discriminate different distributions of data points. The sampling points where the local underlying texture is evaluated are categorized into different texture classes. The points assigned to these classes tend to form connected components in the data space, which are considered as the cores of the clusters.     

基于网格的带有参考参数的聚类算法

提出一种基于网格的带有参考参数的聚类算法,通过密度阈值数组的计算,为用户提供有效的参考参数,不但能满足一般的聚类要求,而且还能将高密度的聚类从低密度的聚类中分离出来,解决了传统网格聚类算法在划分网格时很少考虑数据分布导致聚类质量降低的问题。实验仿真表明,该算法能有效处理任意形状和大小的聚类,很好地识别出孤立点或噪声,并且有较好的精度。     

局部迭代的快速K-means聚类算法

为了解决K-means算法在聚类数量增多的情况下,因选择了不合适的中心初值而影响到聚类效果这一问题,提出了一种局部迭代的快速K-means聚类算法（PIFKM+?）。该算法在K-means聚类的基础上,不断寻找能够被分割的聚类簇和能够被删除的聚类簇,并对受影响的局部数据进行重新聚类处理,降低了整个聚类更新的时间复杂度,提高了聚类的效果。PIFKM+?算法在面对聚类数量众多的情况下,具有能够快速更新聚类、对聚类中心初值不敏感、能够提高聚类精确度等优势。通过与K-means和K-means++两种算法的比较,在仿真数据集和真实数据集的综合实验下,验证了该算法的精确性、高效率性和可扩展性,同时实验结果的统计分析表明该算法在提高了聚类精确度的同时并没有损失太多的时间效率。     

Keyframe-based video summarization using Delaunay clustering

Recent advances in technology have made tremendous amounts of multimedia information available to the general population. An efficient way of dealing with this new development is to develop browsing tools that distill multimedia data as information oriented summaries. Such an approach will not only suit resource poor environments such as wireless and mobile, but also enhance browsing on the wired side for applications like digital libraries and repositories. Automatic summarization and indexing techniques will give users an opportunity to browse and select multimedia document of their choice for complete viewing later. In this paper, we present a technique by which we can automatically gather the frames of interest in a video for purposes of summarization. Our proposed technique is based on using Delaunay Triangulation for clustering the frames in videos. We represent the frame contents as multi-dimensional point data and use Delaunay Triangulation for clustering them. We propose a novel video summarization technique by using Delaunay clusters that generates good quality summaries with fewer frames and less redundancy when compared to other schemes. In contrast to many of the other clustering techniques, the Delaunay clustering algorithm is fully automatic with no user specified parameters and is well suited for batch processing. We demonstrate these and other desirable properties of the proposed algorithm by testing it on a collection of videos from Open Video Project. We provide a meaningful comparison between results of the proposed summarization technique with Open Video storyboard and K-means clustering. We evaluate the results in terms of metrics that measure the content representational value of the proposed technique.     

基于模糊划分测度的聚类有效性指标

聚类有效性指标用于评价聚类结果的有效性。根据聚类的基本特性，提出了一个新的用于发现最优模糊划分的聚类有效性指标，该有效性指标采用模糊划分测度和信息熵两个重要因子来评价模糊聚类的有效性。其中，模糊划分测度用于评价聚类的类内紧致性与类间分离性，而信息熵则反映了模糊聚类划分结果的不确定性程度。实验结果表明，该聚类有效性指标能对模糊聚类结果的有效性进行正确的评价，特别是对于空间数据的聚类有效性评价，同其他有效性指标相比，它不仅能得到最优的模糊划分，而且对权重系数也是不敏感的。     

A new multiobjective clustering technique based on the concepts of stability and symmetry

Most clustering algorithms operate by optimizing (either implicitly or explicitly) a single measure of cluster solution quality. Such methods may perform well on some data sets but lack robustness with respect to variations in cluster shape, proximity, evenness and so forth. In this paper, we have proposed a multiobjective clustering technique which optimizes simultaneously two objectives, one reflecting the total cluster symmetry and the other reflecting the stability of the obtained partitions over different bootstrap samples of the data set. The proposed algorithm uses a recently developed simulated annealing-based multiobjective optimization technique, named AMOSA, as the underlying optimization strategy. Here, points are assigned to different clusters based on a newly defined point symmetry-based distance rather than the Euclidean distance. Results on several artificial and real-life data sets in comparison with another multiobjective clustering technique, MOCK, three single objective genetic algorithm-based automatic clustering techniques, VGAPS clustering, GCUK clustering and HNGA clustering, and several hybrid methods of determining the appropriate number of clusters from data sets show that the proposed technique is well suited to detect automatically the appropriate number of clusters as well as the appropriate partitioning from data sets having point symmetric clusters. The performance of AMOSA as the underlying optimization technique in the proposed clustering algorithm is also compared with PESA-II, another evolutionary multiobjective optimization technique.     

Using automatic process clustering for design recovery anddistributed debugging

Distributed applications written in Hermes typically consist of a large number of sequential processes. The use of a hierarchy of process clusters can facilitate the debugging of such applications. Ideally, such a hierarchy should be derived automatically. This paper discusses two approaches to automatic process clustering, one analyzing runtime information with a statistical approach and one utilizing additional semantic information. Tools realizing these approaches were developed and a quantitative measure to evaluate process clusters is proposed. The results obtained under both approaches are compared, and indicate that the additional semantic information improves the cluster hierarchies derived. We demonstrate the value of automatic process clustering with an example. It is shown how appropriate process clusters reduce the complexity of the understanding process, facilitating program maintenance activities such as debugging     

聚类有效性评价新指标

聚类有效性评价指标分为外部评价指标和内部评价指标两大类。现有外部评价指标没有考虑聚类结果类偏斜现象;现有内部评价指标的聚类有效性检验效果难以得到最佳类簇数。针对现有内外部聚类评价指标的缺陷,提出同时考虑正负类信息的分别基于相依表和样本对的外部评价指标,用于评价任意分布数据集的聚类结果;提出采用方差度量类内紧密度和类间分离度,以类间分离度与类内紧密度之比作为度量指标的内部评价指标。UCI数据集和人工模拟数据集实验测试表明,提出的新内部评价指标能有效发现数据集的真实类簇数;提出的基于相依表和样本对的外部评价指标,可有效评价存在类偏斜与噪音数据的聚类结果。