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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.
Efficient evaluation of queries with mining predicates
 In Proc. of the 18th Int’l Conference on Data Engineering (ICDE
, 2002
"... Modern relational database systems are beginning to support ad hoc queries on mining models. In this paper, we explore novel techniques for optimizing queries that apply mining models to relational data. For such queries, we use the internal structure of the mining model to automatically derive trad ..."
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Cited by 12 (2 self)
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Modern relational database systems are beginning to support ad hoc queries on mining models. In this paper, we explore novel techniques for optimizing queries that apply mining models to relational data. For such queries, we use the internal structure of the mining model to automatically derive traditional database predicates. We present algorithms for deriving such predicates for some popular discrete mining models: decision trees, naive Bayes, and clustering. Our experiments on Microsoft SQL Server 2000 demonstrate that these derived predicates can significantly reduce the cost of evaluating such queries. 1.
Hyperrectanglebased discriminative data generalization and applications in data mining
, 2007
"... The ultimate goal of data mining is to extract knowledge from massive data. Knowledge is ideally represented as humancomprehensible patterns from which endusers can gain intuitions and insights. Axisparallel hyperrectangles provide interpretable generalizations for multidimensional data points ..."
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Cited by 5 (2 self)
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The ultimate goal of data mining is to extract knowledge from massive data. Knowledge is ideally represented as humancomprehensible patterns from which endusers can gain intuitions and insights. Axisparallel hyperrectangles provide interpretable generalizations for multidimensional data points with numerical attributes. In this dissertation, we study the fundamental problem of rectanglebased discriminative data generalization in the context of several useful data mining applications: cluster description, rule learning, and Nearest Rectangle classification. Clustering is one of the most important data mining tasks. However, most clustering methods output sets of points as clusters and do not generalize them into interpretable patterns. We perform a systematic study of cluster description, where we propose novel description formats leading to enhanced expressive power and introduce novel description problems specifying different tradeoffs between interpretability and accuracy. We also present efficient heuristic algorithms for the introduced problems in the proposed formats. Ifthen rules are
An Exact and Efficient Algorithm for the Orthogonal Art Gallery Problem
"... In this paper, we propose an exact algorithm to solve the Orthogonal Art Gallery problem in which guards can only be placed on the vertices of the polygon P representing the gallery. Our approach is based on a discretization of P into a finite set of points in its interior. The algorithm repeatedly ..."
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Cited by 4 (1 self)
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In this paper, we propose an exact algorithm to solve the Orthogonal Art Gallery problem in which guards can only be placed on the vertices of the polygon P representing the gallery. Our approach is based on a discretization of P into a finite set of points in its interior. The algorithm repeatedly solves an instance of the Set Cover problem obtaining a minimum set Z of vertices of P that can view all points in the current discretization. Whenever P is completely visible from Z, the algorithm halts; otherwise, the discretization is refined and another iteration takes place. We establish that the algorithm always converges to an optimal solution by presenting a worst case analysis of the number of iterations that could be effected. Even though these could theoretically reach O(n4), our computational experiments reveal that, in practice, they are linear in n and, for n ≤ 200, they actually remain less than three in almost all instances. Furthermore, the low number of points in the initial discretization, O(n2), compared to the possible O(n4) atomic visibility polygons, renders much shorter total execution times. Optimal solutions found for different classes of instances of polygons with up to 200 vertices are also described. 1. Introduction and Related
Recognizing SStar Polygons
"... We consider the problem of recognizing starpolygons under staircase visibility (s visibility). We show that the svisibility polygon from a point inside a simple orthogonal polygon of n sides can be computed in O(n) time. When the polygon contains holes the algorithm runs in O(n log n) time, w ..."
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We consider the problem of recognizing starpolygons under staircase visibility (s visibility). We show that the svisibility polygon from a point inside a simple orthogonal polygon of n sides can be computed in O(n) time. When the polygon contains holes the algorithm runs in O(n log n) time, which we prove to be optimal by linear time reduction from sorting. We present an algorithm for computing the skernel of a polygon in O(n) time for simple orthogonal polygons and in O(n 2 ) time for orthogonal polygons with holes; both complexities are optimal in the worst case. Finally, we report the main result of this paper: we show that even though the skernel of a polygon with holes may have \Omega\Gamma n 2 ) components it is possible to recognize such polygons in O(n log n) time.
The Generalized MDL Approach for Summarization
, 2002
"... There are many applications in OLAP and data analysis where we identify regions of interest. For example... ..."
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There are many applications in OLAP and data analysis where we identify regions of interest. For example...
Restricted Orientation Visibility
, 1991
"... Let O be some set of orientations, i.e., O ` [0 ffi ; 360 ffi ). In this paper we look at the consequences of defining visibility based on curves that are monotone w.r.t. to the orientations in O. We call such curves Ostaircases. Two points p and q in a polygon P are said to O s see each oth ..."
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Let O be some set of orientations, i.e., O ` [0 ffi ; 360 ffi ). In this paper we look at the consequences of defining visibility based on curves that are monotone w.r.t. to the orientations in O. We call such curves Ostaircases. Two points p and q in a polygon P are said to O s see each other if there exists an Ostaircase from p to q that is completely contained in P. We investigate some of the structural properties of O s visibility and then turn to the computation of the O s kernel of a polygon. The O s kernel of a polygon P is then the set of all points which O s see all other points. We show that the O s kernel of a simple polygon can be obtained as the intersection of all f`g s kernels, with ` 2 O. With the help of this observation we are able to develop an O(n log jOj) algorithm to compute the O s kernel in a simple polygon, for finite O. We also show how to compute the external O s kernel of a polygon in time O(n + jOj). Both algorithms can be ...
1 Handling and Archiving of Theses and Dissertations
, 2009
"... This is to certify that the thesis entitled Polygon and fortress guarding by diffuse reflection, angular visibility and direct visibility, submitted by Arindam Khan(04CS3001), to the department of Computer Science and Engineering in partial fulfillment for the award of the degree of Master of Techno ..."
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This is to certify that the thesis entitled Polygon and fortress guarding by diffuse reflection, angular visibility and direct visibility, submitted by Arindam Khan(04CS3001), to the department of Computer Science and Engineering in partial fulfillment for the award of the degree of Master of Technology, is a bonafide record of work carried out by him under my supervision and guidance. The thesis has fulfilled all the requirements as per the regulations of this institute and, in my opinion, has reached the standard needed for submission.