The Experts below are selected from a list of 267 Experts worldwide ranked by ideXlab platform
Kezhi Mao - One of the best experts on this subject based on the ideXlab platform.
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RBF neural network center selection based on Fisher ratio class separability measure
IEEE transactions on neural networks, 2002Co-Authors: Kezhi MaoAbstract:For classification applications, the role of hidden layer neurons of a radial basis function (RBF) neural network can be interpreted as a function which maps input patterns from a nonlinear Separable Space to a linear Separable Space. In the new Space, the responses of the hidden layer neurons form new feature vectors. The discriminative power is then determined by RBF centers. In the present study, we propose to choose RBF centers based on Fisher ratio class separability measure with the objective of achieving maximum discriminative power. We implement this idea using a multistep procedure that combines Fisher ratio, an orthogonal transform, and a forward selection search method. Our motivation of employing the orthogonal transform is to decouple the correlations among the responses of the hidden layer neurons so that the class separability provided by individual RBF neurons can be evaluated independently. The strengths of our method are double fold. First, our method selects a parsimonious network architecture. Second, this method selects centers that provide large class separation.
Alexander V. Osipov - One of the best experts on this subject based on the ideXlab platform.
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Strongly sequentially Separable function Spaces, via selection principles
Topology and its Applications, 2020Co-Authors: Alexander V. Osipov, Piotr Szewczak, Boaz TsabanAbstract:Abstract A Separable Space is strongly sequentially Separable if, for each countable dense set, every point in the Space is a limit of a sequence from the dense set. We consider this and related properties, for the Spaces of continuous and Borel real-valued functions on Tychonoff Spaces, with the topology of pointwise convergence. Our results solve a problem stated by Gartside, Lo, and Marsh.
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On the different kinds of separability of the Space of Borel functions
Open Mathematics, 2018Co-Authors: Alexander V. OsipovAbstract:AbstractIn paper we prove that:a Space of Borel functions B(X) on a set of reals X, with pointwise topology, to be countably selective sequentially Separable if and only if X has the property S1(BΓ, BΓ);there exists a consistent example of sequentially Separable selectively Separable Space which is not selective sequentially Separable. This is an answer to the question of A. Bella, M. Bonanzinga and M. Matveev;there is a consistent example of a compact T2 sequentially Separable Space which is not selective sequentially Separable. This is an answer to the question of A. Bella and C. Costantini;min{
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On separability of the functional Space with the open-point and bi-point-open topologies
Acta Mathematica Hungarica, 2016Co-Authors: Alexander V. OsipovAbstract:We study the property of separability of functional Space C(X) with the open-point and bi-point-open topologies and show that it is consistent with ZFC that there is a set of reals of cardinality \({\mathfrak{c}}\) such that a set C(X) with the open-point topology is not a Separable Space. We also show in a set model (the iterated perfect set model) that for every set of reals X, C(X) with the bi-point-open topology is a Separable Space.
Xiao Guo - One of the best experts on this subject based on the ideXlab platform.
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The OLS Algorithm Based on Energy Distribution for RBF Neural Network
Computer Science, 2004Co-Authors: Xiao GuoAbstract:: Due to its structural simplicity, the radial basis function (RBF)neural network has been widely used for approximation and classification. The role of hidden layer neurons of a RBF neural network can be interpreted as a function which maps input patterns from a nonlinear Separable Space to a linear Separable Space. In the present study, we use OLS algorithm based on energy distribution to train RBF. The experiment results indicate that the performance of the proposed method is better than that of standard OLS.
Jason Siefken - One of the best experts on this subject based on the ideXlab platform.
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Ergodic optimization of super-continuous functions on shift Spaces
Ergodic Theory and Dynamical Systems, 2011Co-Authors: Anthony Quas, Jason SiefkenAbstract:Ergodic optimization is the process of finding invariant probability measures that maximize the integral of a given function. It has been conjectured that ‘most’ functions are optimized by measures supported on a periodic orbit, and it has been proved in several Separable Spaces that an open and dense subset of functions is optimized by measures supported on a periodic orbit. All known positive results have been for Separable Spaces. We give in this paper the first positive result for a non-Separable Space, the Space of super-continuous functions on the full shift, where the set of functions optimized by periodic orbit measures contains an open dense subset.
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Ergodic Optimization of Super-continuous Functions in the Shift
arXiv: Dynamical Systems, 2011Co-Authors: Anthony Quas, Jason SiefkenAbstract:Ergodic Optimization is the process of finding invariant probability measures that maximize the integral of a given function. It has been conjectured that "most" functions are optimized by measures supported on a periodic orbit, and it has been proved in several Separable Spaces that an open and dense subset of functions is optimized by measures supported on a periodic orbit. We add to these positive results by presenting a non-Separable Space, the class of super-continuous functions, where the set of functions optimized by periodic orbit measures contains an open subset dense in super-continuous functions.
Stefano Federico Tonellato - One of the best experts on this subject based on the ideXlab platform.
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Blur‐generated non‐Separable Space–time models
Journal of the Royal Statistical Society: Series B (Statistical Methodology), 2000Co-Authors: Patrick Brown, Gareth O. Roberts, Kjetil F. Kåresen, Stefano Federico TonellatoAbstract:Statistical Space–time modelling has traditionally been concerned with Separable covariance functions, meaning that the covariance function is a product of a purely temporal function and a purely spatial function. We draw attention to a physical dispersion model which could model phenomena such as the spread of an air pollutant. We show that this model has a non-Separable covariance function. The model is well suited to a wide range of realistic problems which will be poorly fitted by Separable models. The model operates successively in time: the spatial field at time t +1 is obtained by 'blurring' the field at time t and adding a spatial random field. The model is first introduced at discrete time steps, and the limit is taken as the length of the time steps goes to 0. This gives a consistent continuous model with parameters that are interpretable in continuous Space and independent of sampling intervals. Under certain conditions the blurring must be a Gaussian smoothing kernel. We also show that the model is generated by a stochastic differential equation which has been studied by several researchers previously.
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blur generated non Separable Space time models
Journal of The Royal Statistical Society Series B-statistical Methodology, 2000Co-Authors: Patrick Brown, Gareth O. Roberts, Kjetil F. Kåresen, Stefano Federico TonellatoAbstract:Statistical Space–time modelling has traditionally been concerned with Separable covariance functions, meaning that the covariance function is a product of a purely temporal function and a purely spatial function. We draw attention to a physical dispersion model which could model phenomena such as the spread of an air pollutant. We show that this model has a non-Separable covariance function. The model is well suited to a wide range of realistic problems which will be poorly fitted by Separable models. The model operates successively in time: the spatial field at time t +1 is obtained by 'blurring' the field at time t and adding a spatial random field. The model is first introduced at discrete time steps, and the limit is taken as the length of the time steps goes to 0. This gives a consistent continuous model with parameters that are interpretable in continuous Space and independent of sampling intervals. Under certain conditions the blurring must be a Gaussian smoothing kernel. We also show that the model is generated by a stochastic differential equation which has been studied by several researchers previously.
