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28
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 1308 (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.
Automatic Subspace Clustering of High Dimensional Data
 Data Mining and Knowledge Discovery
, 2005
"... Data mining applications place special requirements on clustering algorithms including: the ability to find clusters embedded in subspaces of high dimensional data, scalability, enduser comprehensibility of the results, nonpresumption of any canonical data distribution, and insensitivity to the or ..."
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Cited by 564 (12 self)
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Data mining applications place special requirements on clustering algorithms including: the ability to find clusters embedded in subspaces of high dimensional data, scalability, enduser comprehensibility of the results, nonpresumption of any canonical data distribution, and insensitivity to the order of input records. We present CLIQUE, a clustering algorithm that satisfies each of these requirements. CLIQUE identifies dense clusters in subspaces of maximum dimensionality. It generates cluster descriptions in the form of DNF expressions that are minimized for ease of comprehension. It produces identical results irrespective of the order in which input records are presented and does not presume any specific mathematical form for data distribution. Through experiments, we show that CLIQUE efficiently finds accurate clusters in large high dimensional datasets.
Approximation Algorithms for Projective Clustering
 Proceedings of the ACM SIGMOD International Conference on Management of data, Philadelphia
, 2000
"... We consider the following two instances of the projective clustering problem: Given a set S of n points in R d and an integer k ? 0; cover S by k hyperstrips (resp. hypercylinders) so that the maximum width of a hyperstrip (resp., the maximum diameter of a hypercylinder) is minimized. Let w ..."
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Cited by 246 (21 self)
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We consider the following two instances of the projective clustering problem: Given a set S of n points in R d and an integer k ? 0; cover S by k hyperstrips (resp. hypercylinders) so that the maximum width of a hyperstrip (resp., the maximum diameter of a hypercylinder) is minimized. Let w be the smallest value so that S can be covered by k hyperstrips (resp. hypercylinders), each of width (resp. diameter) at most w : In the plane, the two problems are equivalent. It is NPHard to compute k planar strips of width even at most Cw ; for any constant C ? 0 [50]. This paper contains four main results related to projective clustering: (i) For d = 2, we present a randomized algorithm that computes O(k log k) strips of width at most 6w that cover S. Its expected running time is O(nk 2 log 4 n) if k 2 log k n; it also works for larger values of k, but then the expected running time is O(n 2=3 k 8=3 log 4 n). We also propose another algorithm that computes a c...
An Efficient Approach to Clustering in Large Multimedia Databases with Noise
, 1998
"... Several clustering algorithms can be applied to clustering in large multimedia databases. The effectiveness and efficiency of the existing algorithms, however, is somewhat limited, since clustering in multimedia databases requires clustering highdimensional feature vectors and since multimedia data ..."
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Cited by 207 (9 self)
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Several clustering algorithms can be applied to clustering in large multimedia databases. The effectiveness and efficiency of the existing algorithms, however, is somewhat limited, since clustering in multimedia databases requires clustering highdimensional feature vectors and since multimedia databases often contain large amounts of noise. In this paper, we therefore introduce a new algorithm to clustering in large multimedia databases called DENCLUE (DENsitybased CLUstEring). The basic idea of our new approachis to model the overall point density analytically as the sum of influence functions of the data points. Clusters can then be identified by determining densityattractors and clusters of arbitrary shape can be easily described by a simple equation based on the overall density function. The advantages of our new approach are (1) it has a firm mathematical basis, (2) it has good clustering properties in data sets with large amounts of noise, (3) it allows a compact mathematical ...
Discovery of spatial association rules in geographic information databases
, 1995
"... Abstract. Spatial data mining, i.e., discovery of interesting, implicit knowledge in spatial databases, is an important task for understanding and use of spatial data and knowledgebases. In this paper, an e cient method for mining strong spatial association rules in geographic information database ..."
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Cited by 181 (15 self)
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Abstract. Spatial data mining, i.e., discovery of interesting, implicit knowledge in spatial databases, is an important task for understanding and use of spatial data and knowledgebases. In this paper, an e cient method for mining strong spatial association rules in geographic information databases is proposed and studied. A spatial association rule is a rule indicating certain association relationship among a set of spatial and possibly some nonspatial predicates. A strong rule indicates that the patterns in the rule have relatively frequent occurrences in the database and strong implication relationships. Several optimization techniques are explored, including a twostep spatial computation technique (approximate computation on large sets, and re ned computations on small promising patterns), shared processing in the derivation of large predicates at multiple concept levels, etc. Our analysis shows that interesting association rules can be discovered e ciently in large spatial databases. 1
Outlier detection for high dimensional data
, 2001
"... The outlier detection problem has important applications in the eld of fraud detection, netw ork robustness analysis, and intrusion detection. Most suc h applications are high dimensional domains in whic hthe data can con tain hundreds of dimensions. Many recen t algorithms use concepts of pro ximit ..."
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Cited by 161 (4 self)
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The outlier detection problem has important applications in the eld of fraud detection, netw ork robustness analysis, and intrusion detection. Most suc h applications are high dimensional domains in whic hthe data can con tain hundreds of dimensions. Many recen t algorithms use concepts of pro ximity in order to nd outliers based on their relationship to the rest of the data. Ho w ever, in high dimensional space, the data is sparse and the notion of proximity fails to retain its meaningfulness. In fact, the sparsity of high dimensional data implies that every point is an almost equally good outlier from the perspective ofproximitybased de nitions. Consequently, for high dimensional data, the notion of nding meaningful outliers becomes substantially more complex and nonobvious. In this paper, w e discuss new techniques for outlier detection whic h nd the outliers by studying the behavior of projections from the data set. 1.
DMQL: A Data Mining Query Language for Relational Databases
, 1996
"... The emerging data mining tools and systems lead naturally to the demand of a powerful data mining query language, on top of which manyinteractive and #exible graphical user interfaces can be developed. This motivates us to design a data mining query language, DMQL, for mining di#erent kinds of knowl ..."
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Cited by 126 (6 self)
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The emerging data mining tools and systems lead naturally to the demand of a powerful data mining query language, on top of which manyinteractive and #exible graphical user interfaces can be developed. This motivates us to design a data mining query language, DMQL, for mining di#erent kinds of knowledge in relational databases. Portions of the proposed DMQL language have been implemented in our DBMiner system for interactive mining of multiplelevel knowledge in relational databases. 1 Introduction Data mining is a promising #eld with #ourishing R
Clustering Based On Association Rule Hypergraphs
"... Clustering in data mining is a discovery process that groups a set of data such that the intracluster similarity is maximized and the intercluster similarity is minimized. These discovered clusters are used to explain the characteristics of the data distribution. In this paper we propose a new metho ..."
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Cited by 88 (16 self)
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Clustering in data mining is a discovery process that groups a set of data such that the intracluster similarity is maximized and the intercluster similarity is minimized. These discovered clusters are used to explain the characteristics of the data distribution. In this paper we propose a new methodology for clustering related items using association rules, and clustering related transactions using clusters of items. Our approach is linearly scalable with respect to the number of transactions. The frequent itemsets used to derive association rules are also used to group items into a hypergraph edge, and a hypergraph partitioning algorithm is used to find the clusters. Our experiments indicate that clustering using association rule hypergraphs holds great promise in several application domains. Our experiments with stockmarket data and congressional voting data show that this clustering scheme is able to successfully group items that belong to the same group. Clustering of items can ...
Optimal GridClustering: Towards Breaking the Curse of Dimensionality in HighDimensional Clustering
, 1999
"... Many applications require the clustering of large amounts of highdimensional data. Most clustering algorithms, however, do not work effectively and efficiently in highdimensional space, which is due to the socalled "curse of dimensionality". In addition, the highdimensional data often contains a ..."
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Cited by 85 (4 self)
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Many applications require the clustering of large amounts of highdimensional data. Most clustering algorithms, however, do not work effectively and efficiently in highdimensional space, which is due to the socalled "curse of dimensionality". In addition, the highdimensional data often contains a significant amount of noise which causes additional effectiveness problems. In this paper, we review and compare the existing algorithms for clustering highdimensional data and show the impact of the curse of dimensionality on their effectiveness and efficiency. The comparison reveals that condensationbased approaches (such as BIRCH or STING) are the most promising candidates for achieving the necessary efficiency, but it also shows that basically all condensationbased approaches have severe weaknesses with respect to their effectiveness in highdimensional space. To overcome these problems, we develop a new clustering technique called OptiGrid which is based on constructing an optimal grid...