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

Abstract. We study geometric versions of the min-size k-clustering 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

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 k-point subset such that some measure

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 high-dimensional data. The algorithm provides a computationally efficient ap-proach to nonlinear dimensionality

In this paper we explore some implications of viewing graphs as geometric objects. This approach offers a new perspective on a number of graph-theoretic and algorithmic problems. There are several ways to model graphs geometrically and our main concern here is with geometric representations

, 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

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

is a useful and well-studied 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

We present an algorithm for the 3-center problem in (Rd, L1), i. e., for finding the smallest side length for 3 cubes that cover a given n-point set in Rd, that runs in O(n log n) time for any fixed dimension d. This shows that the problem is fixed-parameter 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 k-center problem in (Rd, L2), for any k> = 2. In particular, we prove that deciding whether a given n-point 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 fixed-parameter 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)).

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