Clustering data with measurement errors

Traditional clustering methods assume that there is no measurement error, or uncertainty, associated with data. Often, however, real world applications require treatment of data that have such errors. In the presence of measurement errors, well-known clustering methods like k-means and hierarchical clustering may not produce satisfactory results.In this article, we develop a statistical model and algorithms for clustering data in the presence of errors. We assume that the errors associated with data follow a multivariate Gaussian distribution and are independent between data points. The model uses the maximum likelihood principle and provides us with a new metric for clustering. This metric is used to develop two algorithms for error-based clustering, hError and kError, that are generalizations of Ward's hierarchical and k-means clustering algorithms, respectively.We discuss types of clustering problems where error information associated with the data to be clustered is readily available and where error-based clustering is likely to be superior to clustering methods that ignore error. We focus on clustering derived data (typically parameter estimates) obtained by fitting statistical models to the observed data. We show that, for Gaussian distributed observed data, the optimal error-based clusters of derived data are the same as the maximum likelihood clusters of the observed data. We also report briefly on two applications with real-world data and a series of simulation studies using four statistical models: (1) sample averaging, (2) multiple linear regression, (3) ARIMA models for time-series, and (4) Markov chains, where error-based clustering performed significantly better than traditional clustering methods.     

Robust data clustering by learning multi-metric Lq-norm distances

Unsupervised clustering for datasets with severe outliers inside is a difficult task. In this approach, we propose a cluster-dependent multi-metric clustering approach which is robust to severe outliers. A dataset is modeled as clusters each contaminated by noises of cluster-dependent unknown noise level in formulating outliers of the cluster. With such a model, a multi-metric Lp-norm transformation is proposed and learnt which maps each cluster to the most Gaussian distribution by minimizing some non-Gaussianity measure. The approach is composed of two consecutive phases: multi-metric location estimation (MMLE) and multi-metric iterative chi-square cutoff (ICSC). Algorithms for MMLE and ICSC are proposed. It is proved that the MMLE algorithm searches for the solution of a multi-objective optimization problem and in fact learns a cluster-dependent multi-metric Lq-norm distance and/or a cluster-dependent multi-kernel defined in data space for each cluster. Experiments on heavy-tailed alpha-stable mixture datasets, Gaussian mixture datasets with radial and diffuse outliers added respectively, and the real Wisconsin breast cancer dataset and lung cancer dataset show that the proposed method is superior to many existent robust clustering and outlier detection methods in both clustering and outlier detection performances.     

融合距离度量和高斯混合模型的中文词义归纳模型

词义归纳是解决词义知识获取的重要研究课题,利用聚类算法对词义进行归纳分析是目前最广泛采用的方法。通过比较K-Means聚类算法和EM聚类算法在 各自 词义归纳模型上的优势,提出一种新的融合距离度量和高斯混合模型的聚类算法,以期利用两种聚类算法分别在距离度量和数据分布计算上的优势,挖掘数据的几何特性和正态分布信息在词义聚类分析中的作用,从而提高词义归纳模型的性能。实验结果表明,所提混合聚类算法对于改进词义归纳模型的性能是十分有效的。     

Clustering data with measurement errors

Traditional clustering methods assume that there is no measurement error, or uncertainty, associated with data. Often, however, real world applications require treatment of data that have such errors. In the presence of measurement errors, well-known clustering methods like k-means and hierarchical clustering may not produce satisfactory results.In this article, we develop a statistical model and algorithms for clustering data in the presence of errors. We assume that the errors associated with data follow a multivariate Gaussian distribution and are independent between data points. The model uses the maximum likelihood principle and provides us with a new metric for clustering. This metric is used to develop two algorithms for error-based clustering, hError and kError, that are generalizations of Ward's hierarchical and k-means clustering algorithms, respectively.We discuss types of clustering problems where error information associated with the data to be clustered is readily available and where error-based clustering is likely to be superior to clustering methods that ignore error. We focus on clustering derived data (typically parameter estimates) obtained by fitting statistical models to the observed data. We show that, for Gaussian distributed observed data, the optimal error-based clusters of derived data are the same as the maximum likelihood clusters of the observed data. We also report briefly on two applications with real-world data and a series of simulation studies using four statistical models: (1) sample averaging, (2) multiple linear regression, (3) ARIMA models for time-series, and (4) Markov chains, where error-based clustering performed significantly better than traditional clustering methods.     

基于密度峰值和近邻优化的聚类算法

针对密度峰值算法在选取聚类中心时的时间复杂度过高,需要人工选择截断距离并且处理流形数据时有可能出现多个密度峰值,导致聚类准确率下降等问题,提出一种新的密度峰值聚类算法,从聚类中心选择、离群点筛选、数据点分配三方面进行讨论和分析,并给出相应的聚类算法。在聚类中心的选择上采取KNN的思想计算数据点的密度,离群点的筛选和剪枝以及数据点分配则利用Voronoi图的性质,结合数据点的分布特征进行处理,并在最后应用层次聚类的思想以合并相似类簇,提高聚类准确率。实验结果表明:所提算法与实验对比算法相比较,具有较好的聚类效果和准确性。     

A novel incremental conceptual hierarchical text clustering method using CFu-tree

As a data mining method, clustering, which is one of the most important tools in information retrieval, organizes data based on unsupervised learning which means that it does not require any training data. But, some text clustering algorithms cannot update existing clusters incrementally and, instead, have to recompute a new clustering from scratch. In view of above, this paper presents a novel down-top incremental conceptual hierarchical text clustering approach using CFu-tree (ICHTC-CF) representation, which starts with each item as a separate cluster. Term-based feature extraction is used for summarizing a cluster in the process. The Comparison Variation measure criterion is also adopted for judging whether the closest pair of clusters can be merged or a previous cluster can be split. And, our incremental clustering method is not sensitive to the input data order. Experimental results show that the performance of our method outperforms k-means, CLIQUE, single linkage clustering and complete linkage clustering, which indicate our new technique is efficient and feasible.     

基于高斯分布的簇间距离计算方法

凝聚的层次聚类算法是一种性能优越的聚类算法,该算法通过不断合并距离相近的簇最终将数据集合划分为用户指定的若干个类别。在聚类的过程中簇间距离计算的准确性是影响算法性能的重要因素。本文提出一种新的基于高斯分布的簇间距离的计算方法,该方法通过簇自身的大小、密度分布等因素改进算法的计算准确性,在不同文本集合上与现有的簇间距离计算方法进行了对比实验,实验结果表明该方法有效地改进了层次聚类算法的性能。     

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.     

Cure: an efficient clustering algorithm for large databases

Clustering, in data mining, is useful for discovering groups and identifying interesting distributions in the underlying data. Traditional clustering algorithms either favor clusters with spherical shapes and similar sizes, or are very fragile in the presence of outliers. We propose a new clustering algorithm called CURE that is more robust to outliers, and identifies clusters having non-spherical shapes and wide variances in size. CURE achieves this by representing each cluster by a certain fixed number of points that are generated by selecting well scattered points from the cluster and then shrinking them toward the center of the cluster by a specified fraction. Having more than one representative point per cluster allows CURE to adjust well to the geometry of non-spherical shapes and the shrinking helps to dampen the effects of outliers. To handle large databases, CURE employs a combination of random sampling and partitioning. A random sample drawn from the data set is first partitioned and each partition is partially clustered. The partial clusters are then clustered in a second pass to yield the desired clusters. Our experimental results confirm that the quality of clusters produced by CURE is much better than those found by existing algorithms. Furthermore, they demonstrate that random sampling and partitioning enable CURE to not only outperform existing algorithms but also to scale well for large databases without sacrificing clustering quality.     

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。     

Using combinatorial optimization in model-based trimmed clustering with cardinality constraints

Statistical clustering criteria with free scale parameters and unknown cluster sizes are inclined to create small, spurious clusters. To mitigate this tendency a statistical model for cardinality-constrained clustering of data with gross outliers is established, its maximum likelihood and maximum a posteriori clustering criteria are derived, and their consistency and robustness are analyzed. The criteria lead to constrained optimization problems that can be solved by using iterative, alternating trimming algorithms of k-means type. Each step in the algorithms requires the solution of a λ-assignment problem known from combinatorial optimization. The method allows one to estimate the numbers of clusters and outliers. It is illustrated with a synthetic data set and a real one.     

Clustering of the self-organizing map using a clustering validity index based on inter-cluster and intra-cluster density

The self-organizing map (SOM) has been widely used in many industrial applications. Classical clustering methods based on the SOM often fail to deliver satisfactory results, specially when clusters have arbitrary shapes. In this paper, through some preprocessing techniques for filtering out noises and outliers, we propose a new two-level SOM-based clustering algorithm using a clustering validity index based on inter-cluster and intra-cluster density. Experimental results on synthetic and real data sets demonstrate that the proposed clustering algorithm is able to cluster data better than the classical clustering algorithms based on the SOM, and find an optimal number of clusters.     

层次非负矩阵分解及在文本聚类中的应用

文本聚类的目标是把数据集中内容相似的文档归为一类,而使内容不同的文档分开。目前针对不同领域的需求,多种解决聚类问题的算法应运而生。然而,由于文本数据本身固有的复杂特点,如海量、高维、稀疏等,使得对海量文本数据的聚类仍然是一个棘手的问题。提出了层次非负矩阵分解聚类方法,该方法不但保留了非负矩阵分解的优点,如同步识别文档类别和找出类别本质特征,而且能够展现类别间的层次结构。这种类别层次结构在网页预览等应用中是非常有用的。在真实数据集20Newsgroups和Reuters-RCV1上的实验结果表明,层次非负矩阵分解相比已有的方法更有效。     

基于多重特征的双层Web用户聚类方法

通过对Web日志的聚类分析,可以发现用户的群体特征,甚至可以预测用户将来的访问模式,进而为不同的用户群提供个性化服务。针对现有方法的一般缺陷,包括特征选择单一无法充分体现用户兴趣偏好和传统Hierarchical算法在用户聚类时存在的收敛效率低、易受用户访问多样性影响的问题,提出了基于多重特征的双层用户聚类方法。该方法采用多重特征对用户相似性进行度量,并在此基础上进行双层聚类。首先采用基于密度的DBSCAN算法来排除用户会话中的离群对象和发现不规则簇,然后再采用自底向上的Hierarchical方法对第一层的聚类结果进行聚类。实验结果表明,本文方法具有良好的稳定性和聚类效果。     

An efficient and scalable family of algorithms for combining clusterings

Clustering is the process of grouping objects that are similar, where similarity between objects is usually measured by a distance metric. The groups formed by a clustering method are referred as clusters. Clustering is a widely used activity with multiple applications ranging from biology to economics. Each clustering technique has some advantages and disadvantages. Some clustering algorithms may even require input parameters which strongly affect the result. In most cases, it is not possible to choose the best distance metric, the best clustering method, and the best input argument values for an input data set. Therefore, multiple clusterings can be obtained by several distance metrics, several clustering methods, and several input argument values. And, multiple clusterings can be combined into a new and better quality final clustering. We propose a family of combining multiple clustering algorithms that are memory efficient, scalable, robust, and intuitive. Our new algorithms offer tremendous speed gain and low memory requirements by working at cluster level, while producing very good quality final clusters. Extensive experimental evaluations on some very challenging artificially generated and real data sets from a diverse set of domains establish the usefulness of our methods.     

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。     

Enhancing minimum spanning tree-based clustering by removing density-based outliers

Traditional minimum spanning tree-based clustering algorithms only make use of information about edges contained in the tree to partition a data set. As a result, with limited information about the structure underlying a data set, these algorithms are vulnerable to outliers. To address this issue, this paper presents a simple while efficient MST-inspired clustering algorithm. It works by finding a local density factor for each data point during the construction of an MST and discarding outliers, i.e., those whose local density factor is larger than a threshold, to increase the separation between clusters. This algorithm is easy to implement, requiring an implementation of iDistance as the only k-nearest neighbor search structure. Experiments performed on both small low-dimensional data sets and large high-dimensional data sets demonstrate the efficacy of our method.     

Characteristic-Based Clustering for Time Series Data

With the growing importance of time series clustering research, particularly for similarity searches amongst long time series such as those arising in medicine or finance, it is critical for us to find a way to resolve the outstanding problems that make most clustering methods impractical under certain circumstances. When the time series is very long, some clustering algorithms may fail because the very notation of similarity is dubious in high dimension space; many methods cannot handle missing data when the clustering is based on a distance metric.This paper proposes a method for clustering of time series based on their structural characteristics. Unlike other alternatives, this method does not cluster point values using a distance metric, rather it clusters based on global features extracted from the time series. The feature measures are obtained from each individual series and can be fed into arbitrary clustering algorithms, including an unsupervised neural network algorithm, self-organizing map, or hierarchal clustering algorithm.Global measures describing the time series are obtained by applying statistical operations that best capture the underlying characteristics: trend, seasonality, periodicity, serial correlation, skewness, kurtosis, chaos, nonlinearity, and self-similarity. Since the method clusters using extracted global measures, it reduces the dimensionality of the time series and is much less sensitive to missing or noisy data. We further provide a search mechanism to find the best selection from the feature set that should be used as the clustering inputs.The proposed technique has been tested using benchmark time series datasets previously reported for time series clustering and a set of time series datasets with known characteristics. The empirical results show that our approach is able to yield meaningful clusters. The resulting clusters are similar to those produced by other methods, but with some promising and interesting variations that can be intuitively explained with knowledge of the global characteristics of the time series.     

一种新的聚类分析算法

给出了一种新的无监督聚类算法,但这种算法并非是基于目标函数的聚类算法,而是对数据直接设计一种迭代运算,以使数据在保持类特征的情况下进行重新组合最终达到分类的目的。通过对一类数据的实验表明,该算法在无监督给出类数方面具有较好的鲁棒性;另外,该算法在数据的准确归类、无监督聚类、确定性,以及对特殊类分布的适用性等方面均优于ＨＣＭ和ＦＣＭ算法,