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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 600 (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.
Xmeans: Extending Kmeans with Efficient Estimation of the Number of Clusters
 In Proceedings of the 17th International Conf. on Machine Learning
, 2000
"... Despite its popularity for general clustering, Kmeans suffers three major shortcomings; it scales poorly computationally, the number of clusters K has to be supplied by the user, and the search is prone to local minima. We propose solutions for the first two problems, and a partial remedy for the t ..."
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Cited by 296 (5 self)
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Despite its popularity for general clustering, Kmeans suffers three major shortcomings; it scales poorly computationally, the number of clusters K has to be supplied by the user, and the search is prone to local minima. We propose solutions for the first two problems, and a partial remedy for the third. Building on prior work for algorithmic acceleration that is not based on approximation, we introduce a new algorithm that efficiently, searches the space of cluster locations and number of clusters to optimize the Bayesian Information Criterion (BIC) or the Akaike Information Criterion (AIC) measure. The innovations include two new ways of exploiting cached sufficient statistics and a new very efficient test that in one Kmeans sweep selects the most promising subset of classes for refinement. This gives rise to a fast, statistically founded algorithm that outputs both the number of classes and their parameters. Experiments show this technique reveals the true number of classes in the underlying distribution, and that it is much faster than repeatedly using accelerated Kmeans for different values of K.
Survey of clustering data mining techniques
, 2002
"... Accrue Software, Inc. Clustering is a division of data into groups of similar objects. Representing the data by fewer clusters necessarily loses certain fine details, but achieves simplification. It models data by its clusters. Data modeling puts clustering in a historical perspective rooted in math ..."
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Cited by 286 (0 self)
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Accrue Software, Inc. Clustering is a division of data into groups of similar objects. Representing the data by fewer clusters necessarily loses certain fine details, but achieves simplification. It models data by its clusters. Data modeling puts clustering in a historical perspective rooted in mathematics, statistics, and numerical analysis. From a machine learning perspective clusters correspond to hidden patterns, the search for clusters is unsupervised learning, and the resulting system represents a data concept. From a practical perspective clustering plays an outstanding role in data mining applications such as scientific data exploration, information retrieval and text mining, spatial database applications, Web analysis, CRM, marketing, medical diagnostics, computational biology, and many others. Clustering is the subject of active research in several fields such as statistics, pattern recognition, and machine learning. This survey focuses on clustering in data mining. Data mining adds to clustering the complications of very large datasets with very many attributes of different types. This imposes unique
Scaling Clustering Algorithms to Large Databasesâ€ť, 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.
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 256 (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...
Efficient Algorithms for Mining Outliers from Large Data Sets
"... In this paper, we propose a novel formulation for distancebased outliers that is based on the distance of a point from its k th nearest neighbor. We rank each point on the basis of its distance to its k th nearest neighbor and declare the top n points in this ranking to be outliers. In addition ..."
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Cited by 250 (1 self)
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In this paper, we propose a novel formulation for distancebased outliers that is based on the distance of a point from its k th nearest neighbor. We rank each point on the basis of its distance to its k th nearest neighbor and declare the top n points in this ranking to be outliers. In addition to developing relatively straightforward solutions to finding such outliers based on the classical nestedloop join and index join algorithms, we develop a highly efficient partitionbased algorithm for mining outliers. This algorithm first partitions the input data set into disjoint subsets, and then prunes entire partitions as soon as it is determined that they cannot contain outliers. This results in substantial savings in computation. We present the results of an extensive experimental study on reallife and synthetic data sets. The results from a reallife NBA database highlight and reveal several expected and unexpected aspects of the database. The results from a study on synthetic data sets demonstrate that the partitionbased algorithm scales well with respect to both data set size and data set dimensionality. 1
Very Fast EMbased Mixture Model Clustering Using Multiresolution kdtrees
 In Advances in Neural Information Processing Systems 11
, 1998
"... Clustering is importantinmany fields including manufacturing, biology, finance, and astronomy. Mixture models are a popular approach due to their statistical foundations, and EM is a very popular method for finding mixture models. EM, however, requires many accesses of the data, and thus has bee ..."
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Cited by 96 (5 self)
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Clustering is importantinmany fields including manufacturing, biology, finance, and astronomy. Mixture models are a popular approach due to their statistical foundations, and EM is a very popular method for finding mixture models. EM, however, requires many accesses of the data, and thus has been dismissed as impractical (e.g. (Zhang, Ramakrishnan, & Livny, 1996)) for data mining of enormous datasets.
Information retrieval on the Web
 ACM Computing Surveys
, 2000
"... In this paper we review studies of the growth of the Internet and technologies that are useful for information search and retrieval on the Web. We present data on the Internet from several different sources, e.g., current as well as projected number of users, hosts, and Web sites. Although numerical ..."
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Cited by 74 (0 self)
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In this paper we review studies of the growth of the Internet and technologies that are useful for information search and retrieval on the Web. We present data on the Internet from several different sources, e.g., current as well as projected number of users, hosts, and Web sites. Although numerical figures vary, overall trends cited
DEMON: Mining and Monitoring Evolving Data
 IEEE Transactions on Knowledge and Data Engineering
, 2000
"... Data mining algorithms have been the focus of much research recently. In practice, the input data to a data mining process resides in a large data warehouse whose data is kept uptodate through periodic or occasional addition and deletion of blocks of data. Most data mining algorithms have either ..."
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Cited by 56 (2 self)
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Data mining algorithms have been the focus of much research recently. In practice, the input data to a data mining process resides in a large data warehouse whose data is kept uptodate through periodic or occasional addition and deletion of blocks of data. Most data mining algorithms have either assumed that the input data is static, or have been designed for arbitrary insertions and deletions of data records.