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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 724 (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.
OPTICS: Ordering Points To Identify the Clustering Structure
, 1999
"... Cluster analysis is a primary method for database mining. It is either used as a standalone tool to get insight into the distribution of a data set, e.g. to focus further analysis and data processing, or as a preprocessing step for other algorithms operating on the detected clusters. Almost all of ..."
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Cited by 511 (49 self)
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Cluster analysis is a primary method for database mining. It is either used as a standalone tool to get insight into the distribution of a data set, e.g. to focus further analysis and data processing, or as a preprocessing step for other algorithms operating on the detected clusters. Almost all of the wellknown clustering algorithms require input parameters which are hard to determine but have a significant influence on the clustering result. Furthermore, for many realdata sets there does not even exist a global parameter setting for which the result of the clustering algorithm describes the intrinsic clustering structure accurately. We introduce a new algorithm for the purpose of cluster analysis which does not produce a clustering of a data set explicitly; but instead creates an augmented ordering of the database representing its densitybased clustering structure. This clusterordering contains information which is equivalent to the densitybased clusterings corresponding to a broad range of parameter settings. It is a versatile basis for both automatic and interactive cluster analysis. We show how to automatically and efficiently extract not only ‘traditional ’ clustering information (e.g. representative points, arbitrary shaped clusters), but also the intrinsic clustering structure. For medium sized data sets, the clusterordering can be represented graphically and for very large data sets, we introduce an appropriate visualization technique. Both are suitable for interactive exploration of the intrinsic clustering structure offering additional insights into the distribution and correlation of the data.
Survey of clustering algorithms
 IEEE TRANSACTIONS ON NEURAL NETWORKS
, 2005
"... Data analysis plays an indispensable role for understanding various phenomena. Cluster analysis, primitive exploration with little or no prior knowledge, consists of research developed across a wide variety of communities. The diversity, on one hand, equips us with many tools. On the other hand, the ..."
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Cited by 483 (4 self)
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Data analysis plays an indispensable role for understanding various phenomena. Cluster analysis, primitive exploration with little or no prior knowledge, consists of research developed across a wide variety of communities. The diversity, on one hand, equips us with many tools. On the other hand, the profusion of options causes confusion. We survey clustering algorithms for data sets appearing in statistics, computer science, and machine learning, and illustrate their applications in some benchmark data sets, the traveling salesman problem, and bioinformatics, a new field attracting intensive efforts. Several tightly related topics, proximity measure, and cluster validation, are also discussed.
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 400 (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
A Framework for Clustering Evolving Data Streams
 In VLDB
, 2003
"... The clustering problem is a difficult problem for the data stream domain. This is because the large volumes of data arriving in a stream renders most traditional algorithms too inefficient. In recent years, a... ..."
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Cited by 353 (35 self)
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The clustering problem is a difficult problem for the data stream domain. This is because the large volumes of data arriving in a stream renders most traditional algorithms too inefficient. In recent years, a...
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 315 (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
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 302 (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...
Discovering Word Senses from Text
 In Proceedings of ACM SIGKDD Conference on Knowledge Discovery and Data Mining
, 2002
"... Inventories of manually compiled dictionaries usually serve as a source for word senses. However, they often include many rare senses while missing corpus/domainspecific senses. We present a clustering algorithm called CBC (Clustering By Committee) that automatically discovers word senses from text ..."
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Cited by 293 (18 self)
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Inventories of manually compiled dictionaries usually serve as a source for word senses. However, they often include many rare senses while missing corpus/domainspecific senses. We present a clustering algorithm called CBC (Clustering By Committee) that automatically discovers word senses from text. It initially discovers a set of tight clusters called committees that are well scattered in the similarity space. The centroid of the members of a committee is used as the feature vector of the cluster. We proceed by assigning words to their most similar clusters. After assigning an element to a cluster, we remove their overlapping features from the element. This allows CBC to discover the less frequent senses of a word and to avoid discovering duplicate senses. Each cluster that a word belongs to represents one of its senses. We also present an evaluation methodology for automatically measuring the precision and recall of discovered senses. Categories and Subject Descriptors H.3.3 [Information Storage and Retrieval]: Information Search and RetrievalClustering.
On Clustering Validation Techniques
 Journal of Intelligent Information Systems
, 2001
"... Cluster analysis aims at identifying groups of similar objects and, therefore helps to discover distribution of patterns and interesting correlations in large data sets. It has been subject of wide research since it arises in many application domains in engineering, business and social sciences. Esp ..."
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Cited by 283 (2 self)
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Cluster analysis aims at identifying groups of similar objects and, therefore helps to discover distribution of patterns and interesting correlations in large data sets. It has been subject of wide research since it arises in many application domains in engineering, business and social sciences. Especially, in the last years the availability of huge transactional and experimental data sets and the arising requirements for data mining created needs for clustering algorithms that scale and can be applied in diverse domains.
Data Clustering: 50 Years Beyond KMeans
, 2008
"... Organizing data into sensible groupings is one of the most fundamental modes of understanding and learning. As an example, a common scheme of scientific classification puts organisms into taxonomic ranks: domain, kingdom, phylum, class, etc.). Cluster analysis is the formal study of algorithms and m ..."
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Cited by 274 (6 self)
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Organizing data into sensible groupings is one of the most fundamental modes of understanding and learning. As an example, a common scheme of scientific classification puts organisms into taxonomic ranks: domain, kingdom, phylum, class, etc.). Cluster analysis is the formal study of algorithms and methods for grouping, or clustering, objects according to measured or perceived intrinsic characteristics or similarity. Cluster analysis does not use category labels that tag objects with prior identifiers, i.e., class labels. The absence of category information distinguishes data clustering (unsupervised learning) from classification or discriminant analysis (supervised learning). The aim of clustering is exploratory in nature to find structure in data. Clustering has a long and rich history in a variety of scientific fields. One of the most popular and simple clustering algorithms, Kmeans, was first published in 1955. In spite of the fact that Kmeans was proposed over 50 years ago and thousands of clustering algorithms have been published since then, Kmeans is still widely used. This speaks to the difficulty of designing a general purpose clustering algorithm and the illposed problem of clustering. We provide a brief overview of clustering, summarize well known clustering methods, discuss the major challenges and key issues in designing clustering algorithms, and point out some of the emerging and useful research directions, including semisupervised clustering, ensemble clustering, simultaneous feature selection, and data clustering and large scale data clustering.