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Multidimensional projection with radial basis function and control points selection

Amorim, Elisa Portes dos Santos; Brazil, Emilio Vital; Nonato, Luis Gustavo; Samavati, Faramarz; Sousa, Mario Costa
Fonte: Keio Universiy, Faculty of Science and Technology; ACM SIGGRAPH; Eurographics; Yokohama Publicador: Keio Universiy, Faculty of Science and Technology; ACM SIGGRAPH; Eurographics; Yokohama
Tipo: Conferência ou Objeto de Conferência
ENG
Relevância na Pesquisa
75.9%
Multidimensional projection techniques provide an appealing approach for multivariate data analysis, for their ability to translate high-dimensional data into a low-dimensional representation that preserves neighborhood information. In recent years, pushed by the ever increasing data complexity in many areas, numerous advances in such techniques have been observed, primarily in terms of computational efficiency and support for interactive applications. Both these achievements were made possible due to the introduction of the concept of control points, which are used in many different multidimensional projection techniques. However, little attention has been drawn towards the process of control points selection. In this work we propose a novel multidimensional projection technique based on radial basis functions (RBF). Our method uses RBF to create a function that maps the data into a low-dimensional space by interpolating the previously calculated position of control points. We also present a built-in method for the control points selection based on “forward-selection” and “Orthogonal Least Squares” techniques. We demonstrate that the proposed selection process allows our technique to work with only a few control points while retaining the projection quality and avoiding redundant control points; Foundation CMG Industrial Research Chair program in Scalable; Alberta Innovates Academy (AITF); NSERC

Multinodal Load Forecasting in Power Electric Systems using a Neural Network with Radial Basis Function

Altran, Alessandra Bonato; Minussi, Carlos Roberto; Martins Lopes, Mara Lucia; Chavarette, Fábio Roberto; Peruzzi, Nelson Jose; Zhou, M
Fonte: Trans Tech Publications Ltd Publicador: Trans Tech Publications Ltd
Tipo: Conferência ou Objeto de Conferência Formato: 39-44
ENG
Relevância na Pesquisa
85.93%
In this paper we present the results of the use of a methodology for multinodal load forecasting through an artificial neural network-type Multilayer Perceptron, making use of radial basis functions as activation function and the Backpropagation algorithm, as an algorithm to train the network. This methodology allows you to make the prediction at various points in power system, considering different types of consumers (residential, commercial, industrial) of the electric grid, is applied to the problem short-term electric load forecasting (24 hours ahead). We use a database (Centralised Dataset - CDS) provided by the Electricity Commission de New Zealand to this work.

Radial basis function network (RBFN) for function approximation

Lucks, M. B.; Oki, N.
Fonte: Universidade Estadual Paulista Publicador: Universidade Estadual Paulista
Tipo: Conferência ou Objeto de Conferência Formato: 1099-1101
ENG
Relevância na Pesquisa
95.99%
A radial basis function network (RBFN) circuit for function approximation is presented. Simulation and experimental results show that the network has good approximation capabilities. The RBFN was a squared hyperbolic secant with three adjustable parameters amplitude, width and center. To test the network a sinusoidal and sinc function was approximated.

Analog implementation of radial basis function network appropriate for transducer linearizer

Lucks, M. B.; Oki, N.
Fonte: Universidade Estadual Paulista Publicador: Universidade Estadual Paulista
Tipo: Conferência ou Objeto de Conferência Formato: 1109-1112
ENG
Relevância na Pesquisa
95.97%
A circuit for transducer linearizer tasks have been designed and built using discrete components and it implements a Radial Basis Function Network (RBFN) with three basis functions. The application in a linearized thermistor showed that the network has good approximation capabilities. The circuit advantages is the amplitude, width and center.

Radial basis function network applied to the linearization of a voltage controlled oscillator

Lucks, Marcio B.; Oki, Nobuo
Fonte: Universidade Estadual Paulista Publicador: Universidade Estadual Paulista
Tipo: Conferência ou Objeto de Conferência Formato: 230-235
ENG
Relevância na Pesquisa
96.06%
An analog circuit that implements a radial basis function network is presented. The proposed circuit allows the adjustment of all shape parameters of the radial functions, i.e., amplitude, center and width. The implemented network was applied to the linearization of a nonlinear circuit, a voltage controlled oscillator (VCO). This application can be classified as an open-loop control in which the network plays the role of the controller. Experimental results have proved the linearization capability of the proposed circuit. Its performance can be improved by using a network with more basis functions. Copyright 2007 ACM.

Radial basis function networks with quantized parameters

Lucks, Marcio B.; Nobuo, Oki
Fonte: Universidade Estadual Paulista Publicador: Universidade Estadual Paulista
Tipo: Conferência ou Objeto de Conferência Formato: 23-27
ENG
Relevância na Pesquisa
75.96%
A RBFN implemented with quantized parameters is proposed and the relative or limited approximation property is presented. Simulation results for sinusoidal function approximation with various quantization levels are shown. The results indicate that the network presents good approximation capability even with severe quantization. The parameter quantization decreases the memory size and circuit complexity required to store the network parameters leading to compact mixed-signal circuits proper for low-power applications. ©2008 IEEE.

RBF circuits based on folded cascode differential pairs

Lucks, Marcio Barbosa; Oki, Nobuo
Fonte: Universidade Estadual Paulista Publicador: Universidade Estadual Paulista
Tipo: Conferência ou Objeto de Conferência Formato: 90-93
ENG
Relevância na Pesquisa
66%
We propose new circuits for the implementation of Radial Basis Functions such as Gaussian and Gaussian-like functions. These RBFs are obtained by the subtraction of two differential pair output currents in a folded cascode configuration. We also propose a multidimensional version based on the unidimensional circuits. SPICE simulation results indicate good functionality. These circuits are intended to be applied in the implementation of radial basis function networks. One possible application of these networks is transducer signal conditioning in aircraft and spacecraft vehicles onboard telemetry systems. Copyright 2008 ACM.

Radial basis function circuits using folded cascode differential pairs

Lucks, Marcio B.; Oki, Nobuo
Fonte: Universidade Estadual Paulista Publicador: Universidade Estadual Paulista
Tipo: Conferência ou Objeto de Conferência Formato: 417-421
ENG
Relevância na Pesquisa
96.02%
In this paper, we propose new circuits for the implementation of Radial Basis Functions (RBF). These RBFs are obtained by the subtraction of two differential pair output currents in a folded cascode configuration. We also propose a multidimensional version based on the unidimensional circuits. SPICE simulation and experimental results indicate good functionality. These circuits are intended to be applied in the implementation of radial basis function networks. Possible applications of these networks include transducer signal conditioning and processing in onboard telemetry systems for aircraft and spacecraft vehicles. © 2010 IEEE.

Proposta de implementação de redes de base radial em tecnologias CMOS e BiCMOS

Lucks, Marcio Barbosa
Fonte: Universidade Estadual Paulista (UNESP) Publicador: Universidade Estadual Paulista (UNESP)
Tipo: Tese de Doutorado Formato: 182 f. : il. fots. (algumas color.)
POR
Relevância na Pesquisa
66.07%
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES); Pós-graduação em Engenharia Elétrica - FEIS; Neste trabalho, apresenta-se o desenvolvimento de redes de base radial em tecnologia CMOS. Para tanto, dois circuitos unidimensionais, denominados RBF1 e RBF2, são propostos. Sua funcionalidade é demonstrada por meio de simulações SPICE e também pela sua implementação prática com a utilização de conjuntos de MOSFETs presentes em circuitos integrados comerciais. Demonstra-se também o desenvolvimento dos circuitos para o caso multidimensional, com o uso de simulações SPICE e a implementação de um circuito RBF1 bidimensional. Além disso, são apresentadas versões dos circuitos RBF1 e RBF2 para tecnologia BiCMOS. Os circuitos propostos são utilizados no projeto de redes de base radial bidimensionais em processo CMOS AMS 0.35 μm. No intuito de testar sua funcionalidade, as redes foram simuladas para algumas aplicações, apresentando bons resultados. A questão da quantização no armazenamento dos parâmetros das redes de base radial e da sua influência na aproximação de funções também é tratada na tese. Foram realizadas várias simulações com diferentes níveis de quantização para algumas tarefas de aproximação de funções. Os resultados obtidos mostram que...

Use of radial basis functions for meshless numerical solutions applied to financial engineering barrier options

Santos,Gisele Tessari; Souza,Maurício Cardoso de; Fortes,Mauri
Fonte: Sociedade Brasileira de Pesquisa Operacional Publicador: Sociedade Brasileira de Pesquisa Operacional
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/08/2009 EN
Relevância na Pesquisa
75.91%
A large number of financial engineering problems involve non-linear equations with non-linear or time-dependent boundary conditions. Despite available analytical solutions, many classical and modified forms of the well-known Black-Scholes (BS) equation require fast and accurate numerical solutions. This work introduces the radial basis function (RBF) method as applied to the solution of the BS equation with non-linear boundary conditions, related to path-dependent barrier options. Furthermore, the diffusional method for solving advective-diffusive equations is explored as to its effectiveness to solve BS equations. Cubic and Thin-Plate Spline (TPS) radial basis functions were employed and evaluated as to their effectiveness to solve barrier option problems. The numerical results, when compared against analytical solutions, allow affirming that the RBF method is very accurate and easy to be implemented. When the RBF method is applied, the diffusional method leads to the same results as those obtained from the classical formulation of Black-Scholes equation.

Design of multiple function antenna array using radial basis function neural network

Reddy,B Rama Sanjeeva; Vakula,D; Sarma,N.V.S.N
Fonte: Sociedade Brasileira de Microondas e Optoeletrônica e Sociedade Brasileira de Eletromagnetismo Publicador: Sociedade Brasileira de Microondas e Optoeletrônica e Sociedade Brasileira de Eletromagnetismo
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/06/2013 EN
Relevância na Pesquisa
95.97%
A novel approach to design Multiple Function Antenna (MFA) arrays using Artificial Neural Networks is suggested. A planar array with uniform current excitations which can generate different beam widths and gains is designed using Artificial Neural Networks. The desired beam width, gain and number of elements are given as input to the neural network. The output of the neural network is the current excitations in the form ON/OFF state of the array. Radial Basis Function Neural Network (RBFNN) is initially trained with the input-output data pairs and tested. The network showed 98% high success rate.

A Radial Basis Function Approach to Financial Time Series Analysis

Hutchinson, James M.
Fonte: MIT - Massachusetts Institute of Technology Publicador: MIT - Massachusetts Institute of Technology
Formato: 160 p.; 681549 bytes; 2849290 bytes; application/octet-stream; application/pdf
EN_US
Relevância na Pesquisa
85.9%
Nonlinear multivariate statistical techniques on fast computers offer the potential to capture more of the dynamics of the high dimensional, noisy systems underlying financial markets than traditional models, while making fewer restrictive assumptions. This thesis presents a collection of practical techniques to address important estimation and confidence issues for Radial Basis Function networks arising from such a data driven approach, including efficient methods for parameter estimation and pruning, a pointwise prediction error estimator, and a methodology for controlling the "data mining' problem. Novel applications in the finance area are described, including customized, adaptive option pricing and stock price prediction.

Comparing Support Vector Machines with Gaussian Kernels to Radial Basis Function Classifiers

Schoelkopf, B.; Sung, K.; Burges, C.; Girosi, F.; Niyogi, P.; Poggio, T.; Vapnik, V.
Fonte: MIT - Massachusetts Institute of Technology Publicador: MIT - Massachusetts Institute of Technology
Formato: 6 p.; 2032389 bytes; 277809 bytes; application/postscript; application/pdf
EN_US
Relevância na Pesquisa
95.93%
The Support Vector (SV) machine is a novel type of learning machine, based on statistical learning theory, which contains polynomial classifiers, neural networks, and radial basis function (RBF) networks as special cases. In the RBF case, the SV algorithm automatically determines centers, weights and threshold such as to minimize an upper bound on the expected test error. The present study is devoted to an experimental comparison of these machines with a classical approach, where the centers are determined by $k$--means clustering and the weights are found using error backpropagation. We consider three machines, namely a classical RBF machine, an SV machine with Gaussian kernel, and a hybrid system with the centers determined by the SV method and the weights trained by error backpropagation. Our results show that on the US postal service database of handwritten digits, the SV machine achieves the highest test accuracy, followed by the hybrid approach. The SV approach is thus not only theoretically well--founded, but also superior in a practical application.

Wire antennas optimizations on various platforms using radial basis functions and evolutionary algorithms.

Zhao, Shifu
Fonte: Universidade de Adelaide Publicador: Universidade de Adelaide
Tipo: Tese de Doutorado
Publicado em //2013
Relevância na Pesquisa
85.9%
High Frequency (HF) and Very High Frequency (VHF) electromagnetic waves have been used as the means of long-distance communication for decades. Nevertheless, in the design of wire antennas for HF and VHF devices, size reduction is one of the critical issues due to wavelengths of in ranges from 1 to 100 meters. It is well known that inductive and capacitive loadings can effectively change the current distribution along an antenna, reducing the self-resonant frequency, and hence the antenna size. Various types of inductive and capacitive loadings can be implemented on the wire antennas using ideal lumped components or realistic winding structures, such as zig-zag and helix shapes. Nevertheless, the physical limits of electrically small antenna can greatly constrain the dimensions, and the design of optimally varying windings will significantly increase the complexity in the modeling and simulation process. Furthermore, size reduction can also introduce significant degradation in both efficiency and bandwidth, and thus, obtaining a design with balanced performance becomes a challenging task, which is addressed in this thesis. The work presented in this thesis contributes to the research by proposing and applying a generic methodology to the optimal design of size-reduced HF and VHF wire antennas. The electromagnetic simulator...

An analog implementation of radial basis function network appropriate for transducer linearizer

Lucks, M. B.; Oki, N.
Fonte: IEEE Publicador: IEEE
Tipo: Conferência ou Objeto de Conferência Formato: 1109-1112
ENG
Relevância na Pesquisa
95.97%
A circuit for transducer linearizer tasks have been designed and built using discrete components and it implements by: a Radial Basis Function Network (RBFN) with three basis functions. The application in a linearized thermistor showed that the network has good approximation capabilities. The circuit advantages is the amplitude, width and center.

An optimal experimental design perspective on redial basis function regression

Fokoue, Ernest; Goel, Prem
Fonte: Rochester Instituto de Tecnologia Publicador: Rochester Instituto de Tecnologia
Tipo: Tese de Doutorado
EN_US
Relevância na Pesquisa
86.03%
This paper provides a new look at radial basis function regression that reveals striking similarities with the traditional optimal experimental design framework. We show theoreti- cally and computationally that the so-called relevant vectors derived through the relevance vector machine (RVM) and corresponding to the centers of the radial basis function net- work, are very similar and often identical to the support points obtained through various optimal experimental design criteria like D-optimality. This allows us to provide a sta- tistical meaning to the relevant centers in the context of radial basis function regression, but also opens the door to a variety of ways of approach optimal experimental design in multivariate settings.

Stable radial basis function selection via mixture modelling of the sample path

Fokoue, Ernest
Fonte: Rochester Instituto de Tecnologia Publicador: Rochester Instituto de Tecnologia
Tipo: Relatório
EN_US
Relevância na Pesquisa
85.96%
We consider a fully Bayesian treatment of radial basis function regression, and propose a solution to the the instability of basis selection. Indeed, when bases are selected solely according to the magnitude of their posterior inclusion probabilities, it is often the case that many bases in the same neighborhood end up getting selected leading to redundancy and ultimately inaccuracy of the representation. In this paper, we propose a straightforward solution to the problem based on post-processing the sample path yielded by the model space search technique. Specifically, we perform an a posteriori model-based clustering of the sample path via a mixture of Gaussians, and then select the points closer to the means of the Gaussians. Our solution is found to be more stable and yields a better performance on simulated and real tasks.

Eigenvalue stability of radial basis function discretizations for time-dependent problems

Platte, R.B.; Driscoll, Tobin A.
Fonte: Department of Mathematical Sciences Publicador: Department of Mathematical Sciences
Tipo: Relatório Formato: 875397 bytes; application/pdf
EN_US
Relevância na Pesquisa
85.9%
Differentiation matrices obtained with infinitely smooth radial basis function (RBF) collo- cation methods have, under many conditions, eigenvalues with positive real part, preventing the use of such methods for time-dependent problems. We explore this difficulty at theoretical and practical levels. Theoretically, we prove that differentiation matrices for conditionally positive definite RBFs are stable for periodic domains. We also show that for Gaussian RBFs, special node distributions can achieve stability in 1-D and tensor-product nonperiodic domains. As a more practical approach for bounded domains, we consider differentiation matrices based on least-squares RBF approximations and show that such schemes can lead to stable methods on less regular nodes. By separating centers and nodes, least-squares techniques open the possibility of the separation of accuracy and stability characteristics.; Supported by NSF DMS-0104229.

Polynomials and their Potential Theory for Gaussian Radial Basis Function Interpolation

Driscoll, Tobin A.; Platte, Rodrigo B.
Fonte: Department of Mathematical Sciences Publicador: Department of Mathematical Sciences
Tipo: Relatório Formato: 667615 bytes; application/pdf
EN_US
Relevância na Pesquisa
75.89%
We explore a connection between Gaussian radial basis functions and polynomials. Using standard tools of potential theory, we find that these radial functions are susceptible to the Runge phenomenon, not only in the limit of increasingly flat functions, but also in the finite shape parameter case. We show that there exist interpolation node distributions that prevent such phenomena and allow stable approximations. Using polynomials also provides an explicit interpolation formula that avoids the difficulties of inverting interpolation matrices, without imposing restrictions on the shape parameter or number of points.; Supported by NSF DMS-0104229

Computing Eigenmodes of Elliptical Operators Using Radial Basis Functions

Platte, Rodrigo B.; Driscoll, Tobin A.
Fonte: Department of Mathematical Sciences Publicador: Department of Mathematical Sciences
Tipo: Relatório Formato: 452812 bytes; application/pdf
EN_US
Relevância na Pesquisa
75.85%
Radial basis function (RBF) approximations have been successfully used to solve boundary-value problems numerically. We show that RBFs can also be used to compute eigenmodes of elliptic operators. Special attention is given to the Laplacian operator in two dimensions. We include techniques to avoid degradation of the solution near the boundaries and corner singularities. Numerical results compare favorably to basic finite element methods.; Supported by NSF grant DMS-0104229.