17,710 research outputs found

    A Survey on Soft Subspace Clustering

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    Subspace clustering (SC) is a promising clustering technology to identify clusters based on their associations with subspaces in high dimensional spaces. SC can be classified into hard subspace clustering (HSC) and soft subspace clustering (SSC). While HSC algorithms have been extensively studied and well accepted by the scientific community, SSC algorithms are relatively new but gaining more attention in recent years due to better adaptability. In the paper, a comprehensive survey on existing SSC algorithms and the recent development are presented. The SSC algorithms are classified systematically into three main categories, namely, conventional SSC (CSSC), independent SSC (ISSC) and extended SSC (XSSC). The characteristics of these algorithms are highlighted and the potential future development of SSC is also discussed.Comment: This paper has been published in Information Sciences Journal in 201

    Methods for fast and reliable clustering

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    On Range Searching with Semialgebraic Sets II

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    Let PP be a set of nn points in Rd\R^d. We present a linear-size data structure for answering range queries on PP with constant-complexity semialgebraic sets as ranges, in time close to O(n11/d)O(n^{1-1/d}). It essentially matches the performance of similar structures for simplex range searching, and, for d5d\ge 5, significantly improves earlier solutions by the first two authors obtained in~1994. This almost settles a long-standing open problem in range searching. The data structure is based on the polynomial-partitioning technique of Guth and Katz [arXiv:1011.4105], which shows that for a parameter rr, 1<rn1 < r \le n, there exists a dd-variate polynomial ff of degree O(r1/d)O(r^{1/d}) such that each connected component of RdZ(f)\R^d\setminus Z(f) contains at most n/rn/r points of PP, where Z(f)Z(f) is the zero set of ff. We present an efficient randomized algorithm for computing such a polynomial partition, which is of independent interest and is likely to have additional applications

    A survey of kernel and spectral methods for clustering

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    Clustering algorithms are a useful tool to explore data structures and have been employed in many disciplines. The focus of this paper is the partitioning clustering problem with a special interest in two recent approaches: kernel and spectral methods. The aim of this paper is to present a survey of kernel and spectral clustering methods, two approaches able to produce nonlinear separating hypersurfaces between clusters. The presented kernel clustering methods are the kernel version of many classical clustering algorithms, e.g., K-means, SOM and neural gas. Spectral clustering arise from concepts in spectral graph theory and the clustering problem is configured as a graph cut problem where an appropriate objective function has to be optimized. An explicit proof of the fact that these two paradigms have the same objective is reported since it has been proven that these two seemingly different approaches have the same mathematical foundation. Besides, fuzzy kernel clustering methods are presented as extensions of kernel K-means clustering algorithm. (C) 2007 Pattem Recognition Society. Published by Elsevier Ltd. All rights reserved
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