**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**2450

# Search results for: 2D function approximation.

##### 2450 Comparison between Beta Wavelets Neural Networks, RBF Neural Networks and Polynomial Approximation for 1D, 2DFunctions Approximation

**Authors:**
Wajdi Bellil,
Chokri Ben Amar,
Adel M. Alimi

**Abstract:**

This paper proposes a comparison between wavelet neural networks (WNN), RBF neural network and polynomial approximation in term of 1-D and 2-D functions approximation. We present a novel wavelet neural network, based on Beta wavelets, for 1-D and 2-D functions approximation. Our purpose is to approximate an unknown function f: Rn - R from scattered samples (xi; y = f(xi)) i=1....n, where first, we have little a priori knowledge on the unknown function f: it lives in some infinite dimensional smooth function space and second the function approximation process is performed iteratively: each new measure on the function (xi; f(xi)) is used to compute a new estimate Ôêºf as an approximation of the function f. Simulation results are demonstrated to validate the generalization ability and efficiency of the proposed Beta wavelet network.

**Keywords:**
Beta wavelets networks,
RBF neural network,
training algorithms,
MSE,
1-D,
2D function approximation.

##### 2449 Particle Swarm Optimization and Quantum Particle Swarm Optimization to Multidimensional Function Approximation

**Authors:**
Diogo Silva,
Fadul Rodor,
Carlos Moraes

**Abstract:**

**Keywords:**
PSO,
QPSO,
function approximation,
AI,
optimization,
multidimensional functions.

##### 2448 A New Approach to Solve Blasius Equation using Parameter Identification of Nonlinear Functions based on the Bees Algorithm (BA)

**Authors:**
E. Assareh,
M.A. Behrang,
M. Ghalambaz,
A.R. Noghrehabadi,
A. Ghanbarzadeh

**Abstract:**

**Keywords:**
Bees Algorithm (BA); Approximate Solutions;
Blasius Differential Equation.

##### 2447 A Note on Negative Hypergeometric Distribution and Its Approximation

**Authors:**
S. B. Mansuri

**Abstract:**

**Keywords:**
Negative hypergeometric distribution,
Poisson distribution,
Poisson approximation,
Stein-Chen identity,
w-function.

##### 2446 Best Co-approximation and Best Simultaneous Co-approximation in Fuzzy Normed Spaces

**Authors:**
J. Kavikumar,
N. S. Manian,
M.B.K. Moorthy

**Abstract:**

The main purpose of this paper is to consider the t-best co-approximation and t-best simultaneous co-approximation in fuzzy normed spaces. We develop the theory of t-best co-approximation and t-best simultaneous co-approximation in quotient spaces. This new concept is employed us to improve various characterisations of t-co-proximinal and t-co-Chebyshev sets.

**Keywords:**
Fuzzy best co-approximation,
fuzzy quotient spaces,
proximinality,
Chebyshevity,
best simultaneous co-approximation.

##### 2445 Definable Subsets in Covering Approximation Spaces

**Authors:**
Xun Ge,
Zhaowen Li

**Abstract:**

**Keywords:**
Covering approximation space,
covering approximation operator,
definable subset,
inner definable subset,
outer definable subset.

##### 2444 Function Approximation with Radial Basis Function Neural Networks via FIR Filter

**Authors:**
Kyu Chul Lee,
Sung Hyun Yoo,
Choon Ki Ahn,
Myo Taeg Lim

**Abstract:**

Recent experimental evidences have shown that because of a fast convergence and a nice accuracy, neural networks training via extended kalman filter (EKF) method is widely applied. However, as to an uncertainty of the system dynamics or modeling error, the performance of the method is unreliable. In order to overcome this problem in this paper, a new finite impulse response (FIR) filter based learning algorithm is proposed to train radial basis function neural networks (RBFN) for nonlinear function approximation. Compared to the EKF training method, the proposed FIR filter training method is more robust to those environmental conditions. Furthermore , the number of centers will be considered since it affects the performance of approximation.

**Keywords:**
Extended kalmin filter (EKF),
classification problem,
radial basis function networks (RBFN),
finite impulse response (FIR)filter.

##### 2443 Multiresolution Approach to Subpixel Registration by Linear Approximation of PSF

**Authors:**
Erol Seke,
Kemal Özkan

**Abstract:**

Linear approximation of point spread function (PSF) is a new method for determining subpixel translations between images. The problem with the actual algorithm is the inability of determining translations larger than 1 pixel. In this paper a multiresolution technique is proposed to deal with the problem. Its performance is evaluated by comparison with two other well known registration method. In the proposed technique the images are downsampled in order to have a wider view. Progressively decreasing the downsampling rate up to the initial resolution and using linear approximation technique at each step, the algorithm is able to determine translations of several pixels in subpixel levels.

**Keywords:**
Point Spread Function,
Subpixel translation,
Superresolution,
Multiresolution approach.

##### 2442 On an Open Problem for Definable Subsets of Covering Approximation Spaces

**Authors:**
Mei He,
Ying Ge,
Jingyu Qian

**Abstract:**

**Keywords:**
Covering approximation space,
covering approximation operator,
definable subset,
inner definable subset,
outer definable subset.

##### 2441 Some Separations in Covering Approximation Spaces

**Authors:**
Xun Ge,
Jinjin Li,
Ying Ge

**Abstract:**

**Keywords:**
Rough set,
covering approximation space,
granularitywise separation.

##### 2440 An Empirical Validation of the Linear- Hyperbolic Approximation of the I-V Characteristic of a Solar Cell Generator

**Authors:**
A. A. Penin

**Abstract:**

An empirical linearly-hyperbolic approximation of the I - V characteristic of a solar cell is presented. This approximation is based on hyperbolic dependence of a current of p-n junctions on voltage for large currents. Such empirical approximation is compared with the early proposed formal linearly-hyperbolic approximation of a solar cell. The expressions defining laws of change of parameters of formal approximation at change of a photo current of family of characteristics are received. It allows simplifying a finding of parameters of approximation on actual curves, to specify their values. Analytical calculation of load regime for linearly - hyperbolic model leads to quadratic equation. Also, this model allows to define soundly a deviation from the maximum power regime and to compare efficiency of regimes of solar cells with different parameters.

**Keywords:**
a solar cell generator,
I − V characteristic,
p − n junction,
approximation

##### 2439 Synthesis of Wavelet Filters using Wavelet Neural Networks

**Authors:**
Wajdi Bellil,
Chokri Ben Amar,
Adel M. Alimi

**Abstract:**

**Keywords:**
Beta wavelets,
Wavenet,
multiresolution analysis,
perfect filter reconstruction,
salient point detect,
repeatability.

##### 2438 Adaptive Impedance Control for Unknown Time-Varying Environment Position and Stiffness

**Authors:**
Norsinnira Zainul Azlan,
Hiroshi Yamaura

**Abstract:**

This study is concerned with a new adaptive impedance control strategy to compensate for unknown time-varying environment stiffness and position. The uncertainties are expressed by Function Approximation Technique (FAT), which allows the update laws to be derived easily using Lyapunov stability theory. Computer simulation results are presented to validate the effectiveness of the proposed strategy.

**Keywords:**
Adaptive Impedance Control,
Function Approximation Technique (FAT),
unknown time-varying environment position and stiffness.

##### 2437 Approximations to the Distribution of the Sample Correlation Coefficient

**Authors:**
John N. Haddad,
Serge B. Provost

**Abstract:**

**Keywords:**
Sample correlation coefficient,
density approximation,
confidence intervals.

##### 2436 Approximation for Average Error Probability of BPSK in the Presence of Phase Error

**Authors:**
Yeonsoo Jang,
Dongweon Yoon,
Ki Ho Kwon,
Jaeyoon Lee,
Wooju Lee

**Abstract:**

**Keywords:**
Average error probability,
Phase shift keying,
Phase
error

##### 2435 Reliability Approximation through the Discretization of Random Variables using Reversed Hazard Rate Function

**Authors:**
Tirthankar Ghosh,
Dilip Roy,
Nimai Kumar Chandra

**Abstract:**

Sometime it is difficult to determine the exact reliability for complex systems in analytical procedures. Approximate solution of this problem can be provided through discretization of random variables. In this paper we describe the usefulness of discretization of a random variable using the reversed hazard rate function of its continuous version. Discretization of the exponential distribution has been demonstrated. Applications of this approach have also been cited. Numerical calculations indicate that the proposed approach gives very good approximation of reliability of complex systems under stress-strength set-up. The performance of the proposed approach is better than the existing discrete concentration method of discretization. This approach is conceptually simple, handles analytic intractability and reduces computational time. The approach can be applied in manufacturing industries for producing high-reliable items.

**Keywords:**
Discretization,
Reversed Hazard Rate,
Exponential
distribution,
reliability approximation,
engineering item.

##### 2434 The Error Analysis of An Upwind Difference Approximation for a Singularly Perturbed Problem

**Authors:**
Jiming Yang

**Abstract:**

An upwind difference approximation is used for a singularly perturbed problem in material science. Based on the discrete Green-s function theory, the error estimate in maximum norm is achieved, which is first-order uniformly convergent with respect to the perturbation parameter. The numerical experimental result is verified the valid of the theoretical analysis.

**Keywords:**
Singularly perturbed,
upwind difference,
uniform convergence.

##### 2433 Adaptive Impedance Control for Unknown Non-Flat Environment

**Authors:**
Norsinnira Zainul Azlan,
Hiroshi Yamaura

**Abstract:**

**Keywords:**
Adaptive impedance control,
Function
Approximation Technique (FAT),
impedance control,
unknown
environment position.

##### 2432 FAT based Adaptive Impedance Control for Unknown Environment Position

**Authors:**
N. Z. Azlan,
H. Yamaura

**Abstract:**

**Keywords:**
Adaptive impedance control,
force based impedance
control,
force control,
Function Approximation Technique (FAT),
unknown environment position.

##### 2431 Blind Image Deconvolution by Neural Recursive Function Approximation

**Authors:**
Jiann-Ming Wu,
Hsiao-Chang Chen,
Chun-Chang Wu,
Pei-Hsun Hsu

**Abstract:**

This work explores blind image deconvolution by recursive function approximation based on supervised learning of neural networks, under the assumption that a degraded image is linear convolution of an original source image through a linear shift-invariant (LSI) blurring matrix. Supervised learning of neural networks of radial basis functions (RBF) is employed to construct an embedded recursive function within a blurring image, try to extract non-deterministic component of an original source image, and use them to estimate hyper parameters of a linear image degradation model. Based on the estimated blurring matrix, reconstruction of an original source image from a blurred image is further resolved by an annealed Hopfield neural network. By numerical simulations, the proposed novel method is shown effective for faithful estimation of an unknown blurring matrix and restoration of an original source image.

**Keywords:**
Blind image deconvolution,
linear shift-invariant(LSI),
linear image degradation model,
radial basis functions (rbf),
recursive function,
annealed Hopfield neural networks.

##### 2430 Constant Factor Approximation Algorithm for p-Median Network Design Problem with Multiple Cable Types

**Authors:**
Chaghoub Soraya,
Zhang Xiaoyan

**Abstract:**

**Keywords:**
Approximation algorithms,
buy-at-bulk,
combinatorial
optimization,
network design,
p-median.

##### 2429 RANFIS : Rough Adaptive Neuro-Fuzzy Inference System

**Authors:**
Sandeep Chandana,
Rene V. Mayorga

**Abstract:**

The paper presents a new hybridization methodology involving Neural, Fuzzy and Rough Computing. A Rough Sets based approximation technique has been proposed based on a certain Neuro – Fuzzy architecture. A New Rough Neuron composition consisting of a combination of a Lower Bound neuron and a Boundary neuron has also been described. The conventional convergence of error in back propagation has been given away for a new framework based on 'Output Excitation Factor' and an inverse input transfer function. The paper also presents a brief comparison of performances, of the existing Rough Neural Networks and ANFIS architecture against the proposed methodology. It can be observed that the rough approximation based neuro-fuzzy architecture is superior to its counterparts.

**Keywords:**
Boundary neuron,
neuro-fuzzy,
output excitation factor,
RANFIS,
rough approximation,
rough neural computing.

##### 2428 Approximation to the Hardy Operator on Topological Measure Spaces

**Authors:**
Kairat T. Mynbaev,
Elena N. Lomakina

**Abstract:**

We consider a Hardy type operator generated by a family of open subsets of a Hausdorff topological space. The family is indexed with non-negative real numbers and is totally ordered. For this operator, we obtain two-sided bounds of its norm, a compactness criterion and bounds for its approximation numbers. Previously bounds for its approximation numbers have been established only in the one-dimensional case, while we do not impose any restrictions on the dimension of the Hausdorff space. The bounds for the norm and conditions for compactness have been found earlier but our approach is different in that we use domain partitions for all problems under consideration.

**Keywords:**
Approximation numbers,
boundedness and
compactness,
multidimensional Hardy operator,
Hausdorff
topological space.

##### 2427 Denoising and Compression in Wavelet Domainvia Projection on to Approximation Coefficients

**Authors:**
Mario Mastriani

**Abstract:**

We describe a new filtering approach in the wavelet domain for image denoising and compression, based on the projections of details subbands coefficients (resultants of the splitting procedure, typical in wavelet domain) onto the approximation subband coefficients (much less noisy). The new algorithm is called Projection Onto Approximation Coefficients (POAC). As a result of this approach, only the approximation subband coefficients and three scalars are stored and/or transmitted to the channel. Besides, with the elimination of the details subbands coefficients, we obtain a bigger compression rate. Experimental results demonstrate that our approach compares favorably to more typical methods of denoising and compression in wavelet domain.

**Keywords:**
Compression,
denoising,
projections,
wavelets.

##### 2426 Multinomial Dirichlet Gaussian Process Model for Classification of Multidimensional Data

**Authors:**
Wanhyun Cho,
Soonja Kang,
Sangkyoon Kim,
Soonyoung Park

**Abstract:**

**Keywords:**
Multinomial dirichlet classification model,
Gaussian
process priors,
variational Bayesian approximation,
Importance
sampling,
approximate posterior distribution,
Marginal likelihood
evidence.

##### 2425 Variational EM Inference Algorithm for Gaussian Process Classification Model with Multiclass and Its Application to Human Action Classification

**Authors:**
Wanhyun Cho,
Soonja Kang,
Sangkyoon Kim,
Soonyoung Park

**Abstract:**

In this paper, we propose the variational EM inference algorithm for the multi-class Gaussian process classification model that can be used in the field of human behavior recognition. This algorithm can drive simultaneously both a posterior distribution of a latent function and estimators of hyper-parameters in a Gaussian process classification model with multiclass. Our algorithm is based on the Laplace approximation (LA) technique and variational EM framework. This is performed in two steps: called expectation and maximization steps. First, in the expectation step, using the Bayesian formula and LA technique, we derive approximately the posterior distribution of the latent function indicating the possibility that each observation belongs to a certain class in the Gaussian process classification model. Second, in the maximization step, using a derived posterior distribution of latent function, we compute the maximum likelihood estimator for hyper-parameters of a covariance matrix necessary to define prior distribution for latent function. These two steps iteratively repeat until a convergence condition satisfies. Moreover, we apply the proposed algorithm with human action classification problem using a public database, namely, the KTH human action data set. Experimental results reveal that the proposed algorithm shows good performance on this data set.

**Keywords:**
Bayesian rule,
Gaussian process classification model
with multiclass,
Gaussian process prior,
human action classification,
laplace approximation,
variational EM algorithm.

##### 2424 The Inverse Problem of Nonsymmetric Matrices with a Submatrix Constraint and its Approximation

**Authors:**
Yongxin Yuan,
Hao Liu

**Abstract:**

In this paper, we first give the representation of the general solution of the following least-squares problem (LSP): Given matrices X ∈ Rn×p, B ∈ Rp×p and A0 ∈ Rr×r, find a matrix A ∈ Rn×n such that XT AX − B = min, s. t. A([1, r]) = A0, where A([1, r]) is the r×r leading principal submatrix of the matrix A. We then consider a best approximation problem: given an n × n matrix A˜ with A˜([1, r]) = A0, find Aˆ ∈ SE such that A˜ − Aˆ = minA∈SE A˜ − A, where SE is the solution set of LSP. We show that the best approximation solution Aˆ is unique and derive an explicit formula for it. Keyw

**Keywords:**
Inverse problem,
Least-squares solution,
model updating,
Singular value decomposition (SVD),
Optimal approximation.

##### 2423 Approximation Algorithm for the Shortest Approximate Common Superstring Problem

**Authors:**
A.S. Rebaï,
M. Elloumi

**Abstract:**

**Keywords:**
Shortest approximate common superstring,
approximation algorithms,
strings overlaps,
complexities.

##### 2422 Properties and Approximation Distribution Reductions in Multigranulation Rough Set Model

**Authors:**
Properties,
Approximation Distribution Reductions in Multigranulation Rough Set Model

**Abstract:**

Some properties of approximation sets are studied in multi-granulation optimist model in rough set theory using maximal compatible classes. The relationships between or among lower and upper approximations in single and multiple granulation are compared and discussed. Through designing Boolean functions and discernibility matrices in incomplete information systems, the lower and upper approximation sets and reduction in multi-granulation environments can be found. By using examples, the correctness of computation approach is consolidated. The related conclusions obtained are suitable for further investigating in multiple granulation RSM.

**Keywords:**
Incomplete information system,
maximal compatible class,
multi-granulation rough set model,
reduction.

##### 2421 On Diffusion Approximation of Discrete Markov Dynamical Systems

**Authors:**
Jevgenijs Carkovs

**Abstract:**

**Keywords:**
Markov dynamical system,
diffusion approximation,
equilibrium stochastic stability.