19,675 research outputs found
Weighted lattice polynomials
We define the concept of weighted lattice polynomial functions as lattice
polynomial functions constructed from both variables and parameters. We provide
equivalent forms of these functions in an arbitrary bounded distributive
lattice. We also show that these functions include the class of discrete Sugeno
integrals and that they are characterized by a median based decomposition
formula.Comment: Revised version (minor changes
A decomposition theorem for maxitive measures
A maxitive measure is the analogue of a finitely additive measure or charge,
in which the usual addition is replaced by the supremum operation. Contrarily
to charges, maxitive measures often have a density. We show that maxitive
measures can be decomposed as the supremum of a maxitive measure with density,
and a residual maxitive measure that is null on compact sets under specific
conditions.Comment: 11 page
A survey of kernel and spectral methods for clustering
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
Extreme phase and rotated quadrature measurements
We determine the extreme points of the convex set of covariant phase
observables. Such extremals describe the best phase parameter measurements of
laser light - the best in the sense that they are free from classical
randomness due to fluctuations in the measuring procedure. We also characterize
extreme fuzzy rotated quadratures
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