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Geometric clustering using the information bottleneck method
 In
, 2004
"... We argue that K–means and deterministic annealing algorithms for geometric clustering can be derived from the more general Information Bottleneck approach. If we cluster the identities of data points to preserve information about their location, the set of optimal solutions is massively degenerate. ..."
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Cited by 8 (4 self)
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We argue that K–means and deterministic annealing algorithms for geometric clustering can be derived from the more general Information Bottleneck approach. If we cluster the identities of data points to preserve information about their location, the set of optimal solutions is massively degenerate
Geometric clustering to minimize the sum of cluster sizes
 In Proc. 13th European Symp. Algorithms, Vol 3669 of LNCS
, 2005
"... Abstract. We study geometric versions of the minsize kclustering problem, a clustering problem which generalizes clustering to minimize the sum of cluster radii and has important applications. We prove that the problem can be solved in polynomial time when the points to be clustered are located on ..."
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Cited by 20 (0 self)
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Abstract. We study geometric versions of the minsize kclustering problem, a clustering problem which generalizes clustering to minimize the sum of cluster radii and has important applications. We prove that the problem can be solved in polynomial time when the points to be clustered are located
Efficient Parallel Algorithms for Geometric Clustering and Partitioning Problems
, 1994
"... We present efficient parallel algorithms for some geometric clustering and partitioning problems. Our algorithms run in the CREW PRAM model of parallel computation. Given a point set P of n points in two dimensions, the clustering problems are to find a kpoint subset such that some measure for ..."
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Cited by 3 (0 self)
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We present efficient parallel algorithms for some geometric clustering and partitioning problems. Our algorithms run in the CREW PRAM model of parallel computation. Given a point set P of n points in two dimensions, the clustering problems are to find a kpoint subset such that some measure
Laplacian Eigenmaps for Dimensionality Reduction and Data Representation
, 2003
"... One of the central problems in machine learning and pattern recognition is to develop appropriate representations for complex data. We consider the problem of constructing a representation for data lying on a lowdimensional manifold embedded in a highdimensional space. Drawing on the correspondenc ..."
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Cited by 1226 (15 self)
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on the correspondence between the graph Laplacian, the Laplace Beltrami operator on the manifold, and the connections to the heat equation, we propose a geometrically motivated algorithm for representing the highdimensional data. The algorithm provides a computationally efficient approach to nonlinear dimensionality
The geometry of graphs and some of its algorithmic applications
 COMBINATORICA
, 1995
"... In this paper we explore some implications of viewing graphs as geometric objects. This approach offers a new perspective on a number of graphtheoretic and algorithmic problems. There are several ways to model graphs geometrically and our main concern here is with geometric representations that res ..."
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Cited by 524 (19 self)
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In this paper we explore some implications of viewing graphs as geometric objects. This approach offers a new perspective on a number of graphtheoretic and algorithmic problems. There are several ways to model graphs geometrically and our main concern here is with geometric representations
Features of similarity.
 Psychological Review
, 1977
"... Similarity plays a fundamental role in theories of knowledge and behavior. It serves as an organizing principle by which individuals classify objects, form concepts, and make generalizations. Indeed, the concept of similarity is ubiquitous in psychological theory. It underlies the accounts of stimu ..."
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Cited by 1455 (2 self)
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, errors of substitution, and correlation between occurrences. Analyses of these data attempt to explain the observed similarity relations and to capture the underlying structure of the objects under study. The theoretical analysis of similarity relations has been dominated by geometric models
A Fast Geometric Clustering Method on Conformation Space of
"... Modern computer simulations can easily generate massive data sets with millions of conformations, making analysis of them computationally challenging. Structure based clustering is one approach to reduce the complexity of the data by grouping conformations of similar structure into the same cluster. ..."
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Modern computer simulations can easily generate massive data sets with millions of conformations, making analysis of them computationally challenging. Structure based clustering is one approach to reduce the complexity of the data by grouping conformations of similar structure into the same cluster
Geometric Clustering for Multiplicative Mixtures of Distributions in Exponential Families (Extended Abstract)
"... ) Mary Inaba and Hiroshi Imai Department of Information Science, University of Tokyo Hongo, Bunkyoku, Tokyo, 1130033 Japan. Email: fmary,imaig@is.s.utokyo.ac.jp 1 Introduction Estimating unknown parameters from observed data generated by a mixture of distributions in the exponential family is a ..."
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Cited by 2 (0 self)
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is a useful and wellstudied problem in statistics [1, 2, 7, 8]. This paper investigates this problem from the viewpoint of computational geometry. We define an analogue to the problem in a setting of geometric clustering, specifically introduce a multiplicative version of the likelihood function
Geometric Clustering: FixedParameter Tractability and Lower Bounds with Respect to the Dimension
"... We present an algorithm for the 3center problem in (Rd, L1), i. e., for finding the smallest side length for 3 cubes that cover a given npoint set in Rd, that runs in O(n log n) time for any fixed dimension d. This shows that the problem is fixedparameter tractable when parameterized with d. On ..."
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Cited by 7 (6 self)
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We present an algorithm for the 3center problem in (Rd, L1), i. e., for finding the smallest side length for 3 cubes that cover a given npoint set in Rd, that runs in O(n log n) time for any fixed dimension d. This shows that the problem is fixedparameter tractable when parameterized with d. On the other hand, using tools from parameterized complexity theory, we show that this is unlikely to be the case with the kcenter problem in (Rd, L2), for any k> = 2. In particular, we prove that deciding whether a given npoint set in Rd can be covered by the union of 2 balls of given radius is W[1]hard with respect to d, and thus not fixedparameter tractable unless FPT=W[1]. Our reduction also shows that even an O(no(d))time algorithm for the latter does not exist, unless SNP ae DTIME(2o(n)).
DivergenceBased Geometric Clustering and Its Underlying Discrete Proximity Structures
, 2000
"... This paper sur eysrsfiA tprSNSLfi in the investigation of the under#fi5# discr# pr ximitystr"Mfi5#Y of geometrN ..."
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This paper sur eysrsfiA tprSNSLfi in the investigation of the under#fi5# discr# pr ximitystr"Mfi5#Y of geometrN
Results 11  20
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