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138
Data Clustering: A Review
 ACM COMPUTING SURVEYS
, 1999
"... Clustering is the unsupervised classification of patterns (observations, data items, or feature vectors) into groups (clusters). The clustering problem has been addressed in many contexts and by researchers in many disciplines; this reflects its broad appeal and usefulness as one of the steps in exp ..."
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Cited by 1413 (13 self)
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Clustering is the unsupervised classification of patterns (observations, data items, or feature vectors) into groups (clusters). The clustering problem has been addressed in many contexts and by researchers in many disciplines; this reflects its broad appeal and usefulness as one of the steps in exploratory data analysis. However, clustering is a difficult problem combinatorially, and differences in assumptions and contexts in different communities has made the transfer of useful generic concepts and methodologies slow to occur. This paper presents an overview of pattern clustering methods from a statistical pattern recognition perspective, with a goal of providing useful advice and references to fundamental concepts accessible to the broad community of clustering practitioners. We present a taxonomy of clustering techniques, and identify crosscutting themes and recent advances. We also describe some important applications of clustering algorithms such as image segmentation, object recognition, and information retrieval.
Mean shift, mode seeking, and clustering
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1995
"... AbstractMean shift, a simple iterative procedure that shifts each data point to the average of data points in its neighborhood, is generalized and analyzed in this paper. This generalization makes some kmeans like clustering algorithms its special cases. It is shown that mean shift is a modeseeki ..."
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Cited by 428 (0 self)
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AbstractMean shift, a simple iterative procedure that shifts each data point to the average of data points in its neighborhood, is generalized and analyzed in this paper. This generalization makes some kmeans like clustering algorithms its special cases. It is shown that mean shift is a modeseeking process on a surface constructed with a “shadow ” kernel. For Gaussian kernels, mean shift is a gradient mapping. Convergence is studied for mean shift iterations. Cluster analysis is treated as a deterministic problem of finding a fixed point of mean shift that characterizes the data. Applications in clustering and Hough transform are demonstrated. Mean shift is also considered as an evolutionary strategy that performs multistart global optimization. Index TermsMean shift, gradient descent, global optimization, Hough transform, cluster analysis, kmeans clustering. I.
Centroidal Voronoi tessellations: Applications and algorithms
 SIAM Rev
, 1999
"... Abstract. A centroidal Voronoi tessellation is a Voronoi tessellation whose generating points are the centroids (centers of mass) of the corresponding Voronoi regions. We give some applications of such tessellations to problems in image compression, quadrature, finite difference methods, distributio ..."
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Cited by 264 (28 self)
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Abstract. A centroidal Voronoi tessellation is a Voronoi tessellation whose generating points are the centroids (centers of mass) of the corresponding Voronoi regions. We give some applications of such tessellations to problems in image compression, quadrature, finite difference methods, distribution of resources, cellular biology, statistics, and the territorial behavior of animals. We discuss methods for computing these tessellations, provide some analyses concerning both the tessellations and the methods for their determination, and, finally, present the results of some numerical experiments.
Scaling Clustering Algorithms to Large Databases”, Microsoft Research Report
, 1998
"... Practical clustering algorithms require multiple data scans to achieve convergence. For large databases, these scans become prohibitively expensive. We present a scalable clustering framework applicable to a wide class of iterative clustering. We require at most one scan of the database. In this wor ..."
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Cited by 259 (5 self)
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Practical clustering algorithms require multiple data scans to achieve convergence. For large databases, these scans become prohibitively expensive. We present a scalable clustering framework applicable to a wide class of iterative clustering. We require at most one scan of the database. In this work, the framework is instantiated and numerically justified with the popular KMeans clustering algorithm. The method is based on identifying regions of the data that are compressible, regions that must be maintained in memory, and regions that are discardable. The algorithm operates within the confines of a limited memory buffer. Empirical results demonstrate that the scalable scheme outperforms a samplingbased approach. In our scheme, data resolution is preserved to the extent possible based upon the size of the allocated memory buffer and the fit of current clustering model to the data. The framework is naturally extended to update multiple clustering models simultaneously. We empirically evaluate on synthetic and publicly available data sets.
Refining Initial Points for KMeans Clustering
, 1998
"... Practical approaches to clustering use an iterative procedure (e.g. KMeans, EM) which converges to one of numerous local minima. It is known that these iterative techniques are especially sensitive to initial starting conditions. We present a procedure for computing a refined starting condition fro ..."
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Cited by 250 (5 self)
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Practical approaches to clustering use an iterative procedure (e.g. KMeans, EM) which converges to one of numerous local minima. It is known that these iterative techniques are especially sensitive to initial starting conditions. We present a procedure for computing a refined starting condition from a given initial one that is based on an efficient technique for estimating the modes of a distribution. The refined initial starting condition allows the iterative algorithm to converge to a "better" local minimum. The procedure is applicable to a wide class of clustering algorithms for both discrete and continuous data. We demonstrate the application of this method to the popular KMeans clustering algorithm and show that refined initial starting points indeed lead to improved solutions. Refinement run time is considerably lower than the time required to cluster the full database. The method is scalable and can be coupled with a scalable clustering algorithm to address the largescale cl...
Efficient Identification of Web Communities
 In Sixth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining
, 2000
"... We de ne a community on the web as a set of sites that have more links (in either direction) to members of the community than to nonmembers. Members of such a community can be eciently identi ed in a maximum ow / minimum cut framework, where the source is composed of known members, and the sink c ..."
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Cited by 249 (12 self)
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We de ne a community on the web as a set of sites that have more links (in either direction) to members of the community than to nonmembers. Members of such a community can be eciently identi ed in a maximum ow / minimum cut framework, where the source is composed of known members, and the sink consists of wellknown nonmembers. A focused crawler that crawls to a xed depth can approximate community membership by augmenting the graph induced by the crawl with links to a virtual sink node. The effectiveness of the approximation algorithm is demonstrated with several crawl results that identify hubs, authorities, web rings, and other link topologies that are useful but not easily categorized. Applications of our approach include focused crawlers and search engines, automatic population of portal categories, and improved ltering.
An Efficient kMeans Clustering Algorithm: Analysis and Implementation
, 2000
"... Kmeans clustering is a very popular clustering technique, which is used in numerous applications. Given a set of n data points in R d and an integer k, the problem is to determine a set of k points R d , called centers, so as to minimize the mean squared distance from each data point to its ..."
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Cited by 241 (4 self)
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Kmeans clustering is a very popular clustering technique, which is used in numerous applications. Given a set of n data points in R d and an integer k, the problem is to determine a set of k points R d , called centers, so as to minimize the mean squared distance from each data point to its nearest center. A popular heuristic for kmeans clustering is Lloyd's algorithm. In this paper we present a simple and efficient implementation of Lloyd's kmeans clustering algorithm, which we call the filtering algorithm. This algorithm is very easy to implement. It differs from most other approaches in that it precomputes a kdtree data structure for the data points rather than the center points. We establish the practical efficiency of the filtering algorithm in two ways. First, we present a datasensitive analysis of the algorithm's running time. Second, we have implemented the algorithm and performed a number of empirical studies, both on synthetically generated data and on real...
Extensions to the kMeans Algorithm for Clustering Large Data Sets with Categorical Values
, 1998
"... The kmeans algorithm is well known for its efficiency in clustering large data sets. However, working only on numeric values prohibits it from being used to cluster real world data containing categorical values. In this paper we present two algorithms which extend the kmeans algorithm to categoric ..."
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Cited by 174 (3 self)
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The kmeans algorithm is well known for its efficiency in clustering large data sets. However, working only on numeric values prohibits it from being used to cluster real world data containing categorical values. In this paper we present two algorithms which extend the kmeans algorithm to categorical domains and domains with mixed numeric and categorical values. The kmodes algorithm uses a simple matching dissimilarity measure to deal with categorical objects, replaces the means of clusters with modes, and uses a frequencybased method to update modes in the clustering process to minimise the clustering cost function. With these extensions the kmodes algorithm enables the clustering of categorical data in a fashion similar to kmeans. The kprototypes algorithm, through the definition of a combined dissimilarity measure, further integrates the kmeans and kmodes algorithms to allow for clustering objects described by mixed numeric and categorical attributes. We use the well known soybean disease and credit approval data sets to demonstrate the clustering performance of the two algorithms. Our experiments on two real world data sets with half a million objects each show that the two algorithms are efficient when clustering large data sets, which is critical to data mining applications.
Clustering with instancelevel constraints
 In Proceedings of the Seventeenth International Conference on Machine Learning
, 2000
"... One goal of research in artificial intelligence is to automate tasks that currently require human expertise; this automation is important because it saves time and brings problems that were previously too large to be solved into the feasible domain. Data analysis, or the ability to identify meaningf ..."
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Cited by 164 (6 self)
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One goal of research in artificial intelligence is to automate tasks that currently require human expertise; this automation is important because it saves time and brings problems that were previously too large to be solved into the feasible domain. Data analysis, or the ability to identify meaningful patterns and trends in large volumes of data, is an important task that falls into this category. Clustering algorithms are a particularly useful group of data analysis tools. These methods are used, for example, to analyze satellite images of the Earth to identify and categorize different land and foliage types or to analyze telescopic observations to determine what distinct types of astronomical bodies exist and to categorize each observation. However, most existing clustering methods apply general similarity techniques rather than making use of problemspecific information. This dissertation first presents a novel method for converting existing clustering algorithms into constrained clustering algorithms. The resulting methods are able to accept domainspecific information in the form of constraints on the output clusters. At the most general level, each constraint is an instancelevel statement
An Empirical Comparison of Four Initialization Methods for the KMeans Algorithm
, 1999
"... In this paper, we aim to compare empirically four initialization methods for the KMeans algorithm: random, Forgy, MacQueen and Kaufman. Although this algorithm is known for its robustness, it is widely reported in literature that its performance depends upon two key points: initial clustering an ..."
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Cited by 106 (0 self)
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In this paper, we aim to compare empirically four initialization methods for the KMeans algorithm: random, Forgy, MacQueen and Kaufman. Although this algorithm is known for its robustness, it is widely reported in literature that its performance depends upon two key points: initial clustering and instance order. We conduct a series of experiments to draw up (in terms of mean, maximum, minimum and standard deviation) the probability distribution of the squareerror values of the final clusters returned by the KMeans algorithm independently on any initial clustering and on any instance order when each of the four initialization methods is used. The results of our experiments illustrate that the random and the Kaufman initialization methods outperform the rest of the compared methods as they make the KMeans more effective and more independent on initial clustering and on instance order. In addition, we compare the convergence speed of the KMeans algorithm when using each o...