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Mining Quantitative Association Rules in Large Relational Tables
, 1996
"... We introduce the problem of mining association rules in large relational tables containing both quantitative and categorical attributes. An example of such an association might be "10% of married people between age 50 and 60 have at least 2 cars". We deal with quantitative attributes by finepartitio ..."
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Cited by 348 (3 self)
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We introduce the problem of mining association rules in large relational tables containing both quantitative and categorical attributes. An example of such an association might be "10% of married people between age 50 and 60 have at least 2 cars". We deal with quantitative attributes by finepartitioning the values of the attribute and then combining adjacent partitions as necessary. We introduce measures of partial completeness which quantify the information lost due to partitioning. A direct application of this technique can generate too many similar rules. We tackle this problem by using a "greaterthanexpectedvalue" interest measure to identify the interesting rules in the output. We give an algorithm for mining such quantitative association rules. Finally, we describe the results of using this approach on a reallife dataset. 1 Introduction Data mining, also known as knowledge discovery in databases, has been recognized as a new area for database research. The problem of discove...
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 340 (45 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.
Constrained Kmeans Clustering with Background Knowledge
 In ICML
, 2001
"... Clustering is traditionally viewed as an unsupervised method for data analysis. However, in some cases information about the problem domain is available in addition to the data instances themselves. In this paper, we demonstrate how the popular kmeans clustering algorithm can be pro tably modi ed ..."
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Cited by 326 (9 self)
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Clustering is traditionally viewed as an unsupervised method for data analysis. However, in some cases information about the problem domain is available in addition to the data instances themselves. In this paper, we demonstrate how the popular kmeans clustering algorithm can be pro tably modi ed to make use of this information. In experiments with arti cial constraints on six data sets, we observe improvements in clustering accuracy. We also apply this method to the realworld problem of automatically detecting road lanes from GPS data and observe dramatic increases in performance. 1.
Searching in Metric Spaces
, 1999
"... The problem of searching the elements of a set which are close to a given query element under some similarity criterion has a vast number of applications in many branches of computer science, from pattern recognition to textual and multimedia information retrieval. We are interested in the rather ge ..."
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Cited by 321 (34 self)
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The problem of searching the elements of a set which are close to a given query element under some similarity criterion has a vast number of applications in many branches of computer science, from pattern recognition to textual and multimedia information retrieval. We are interested in the rather general case where the similarity criterion defines a metric space, instead of the more restricted case of a vector space. A large number of solutions have been proposed in different areas, in many cases without crossknowledge. Because of this, the same ideas have been reinvented several times, and very different presentations have been given for the same approaches. We
Clustering with Bregman Divergences
 JOURNAL OF MACHINE LEARNING RESEARCH
, 2005
"... A wide variety of distortion functions are used for clustering, e.g., squared Euclidean distance, Mahalanobis distance and relative entropy. In this paper, we propose and analyze parametric hard and soft clustering algorithms based on a large class of distortion functions known as Bregman divergence ..."
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Cited by 310 (52 self)
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A wide variety of distortion functions are used for clustering, e.g., squared Euclidean distance, Mahalanobis distance and relative entropy. In this paper, we propose and analyze parametric hard and soft clustering algorithms based on a large class of distortion functions known as Bregman divergences. The proposed algorithms unify centroidbased parametric clustering approaches, such as classical kmeans and informationtheoretic clustering, which arise by special choices of the Bregman divergence. The algorithms maintain the simplicity and scalability of the classical kmeans algorithm, while generalizing the basic idea to a very large class of clustering loss functions. There are two main contributions in this paper. First, we pose the hard clustering problem in terms of minimizing the loss in Bregman information, a quantity motivated by ratedistortion theory, and present an algorithm to minimize this loss. Secondly, we show an explicit bijection between Bregman divergences and exponential families. The bijection enables the development of an alternative interpretation of an ecient EM scheme for learning models involving mixtures of exponential distributions. This leads to a simple soft clustering algorithm for all Bregman divergences.
From data mining to knowledge discovery in databases
 AI Magazine
, 1996
"... ■ Data mining and knowledge discovery in databases have been attracting a significant amount of research, industry, and media attention of late. What is all the excitement about? This article provides an overview of this emerging field, clarifying how data mining and knowledge discovery in databases ..."
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Cited by 295 (0 self)
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■ Data mining and knowledge discovery in databases have been attracting a significant amount of research, industry, and media attention of late. What is all the excitement about? This article provides an overview of this emerging field, clarifying how data mining and knowledge discovery in databases are related both to each other and to related fields, such as machine learning, statistics, and databases. The article mentions particular realworld applications, specific datamining techniques, challenges involved in realworld applications of knowledge discovery, and current and future research directions in the field. Across a wide variety of fields, data are
Unsupervised learning of finite mixture models
 IEEE Transactions on pattern analysis and machine intelligence
, 2002
"... AbstractÐThis paper proposes an unsupervised algorithm for learning a finite mixture model from multivariate data. The adjective ªunsupervisedº is justified by two properties of the algorithm: 1) it is capable of selecting the number of components and 2) unlike the standard expectationmaximization ..."
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Cited by 267 (20 self)
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AbstractÐThis paper proposes an unsupervised algorithm for learning a finite mixture model from multivariate data. The adjective ªunsupervisedº is justified by two properties of the algorithm: 1) it is capable of selecting the number of components and 2) unlike the standard expectationmaximization (EM) algorithm, it does not require careful initialization. The proposed method also avoids another drawback of EM for mixture fitting: the possibility of convergence toward a singular estimate at the boundary of the parameter space. The novelty of our approach is that we do not use a model selection criterion to choose one among a set of preestimated candidate models; instead, we seamlessly integrate estimation and model selection in a single algorithm. Our technique can be applied to any type of parametric mixture model for which it is possible to write an EM algorithm; in this paper, we illustrate it with experiments involving Gaussian mixtures. These experiments testify for the good performance of our approach. Index TermsÐFinite mixtures, unsupervised learning, model selection, minimum message length criterion, Bayesian methods, expectationmaximization algorithm, clustering. æ 1
InformationTheoretic CoClustering
 In KDD
, 2003
"... Twodimensional contingency or cooccurrence tables arise frequently in important applications such as text, weblog and marketbasket data analysis. A basic problem in contingency table analysis is coclustering: simultaneous clustering of the rows and columns. A novel theoretical formulation views ..."
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Cited by 249 (11 self)
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Twodimensional contingency or cooccurrence tables arise frequently in important applications such as text, weblog and marketbasket data analysis. A basic problem in contingency table analysis is coclustering: simultaneous clustering of the rows and columns. A novel theoretical formulation views the contingency table as an empirical joint probability distribution of two discrete random variables and poses the coclustering problem as an optimization problem in information theory  the optimal coclustering maximizes the mutual information between the clustered random variables subject to constraints on the number of row and column clusters.
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 247 (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
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...