Vector field radial basis function approximation

Smolik, Michal; Skala, Václav; Majdisova, Zuzana

doi:10.1016/j.advengsoft.2018.06.013

Cited by 18 publications

(8 citation statements)

References 27 publications

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“…The Radial Basis Function (RBF) interpolation [ 18 ] and approximation [ 8 ] is a meshless technique which was introduced by Hardy [ 13 ]. It is commonly used in many scientific disciplines such as solution of partial differential equations [ 14 , 32 ], image reconstruction [ 29 ], neural networks [ 31 ], vector field [ 24 , 26 , 27 ], GIS systems [ 16 ], optics [ 19 ] etc.…”

Section: Radial Basis Functionsmentioning

confidence: 99%

Efficient Speed-Up of Radial Basis Functions Approximation and Interpolation Formula Evaluation

Smolik

Skala

2020

Computational Science and Its Applications – ICCSA 2020

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This paper presents a method for efficient Radial basis function (RBF) evaluation if compactly supported radial basis functions (CSRBF) are used. Application of CSRBF leads to sparse matrices, due to limited influence of radial basis functions in the data domain and thus non-zero weights (coefficients) are valid only for some areas in the data domain. The presented algorithm uses space subdivision which enables us to use only relevant weights for efficient RBF function evaluation. This approach is applicable for 2 D and 3 D case and leads to a significant speed-up. This approach is applicable in cases when the RBF function is evaluated repeatably.

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Section: Radial Basis Functionsmentioning

confidence: 99%

Efficient Speed-Up of Radial Basis Functions Approximation and Interpolation Formula Evaluation

Smolik

Skala

2020

Computational Science and Its Applications – ICCSA 2020

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“…One of the best features of neural networks is its ability to generalize and approximate a sample data without the need of specify equation and coefficients, particularly when an unknown model describing an unknown complex relation and training data abundant. Due to their ability to generalize substantially, Radial Basis Function networks (RBFN) are usually selected for this purpose [9][10][11][12][13][14][15][16][17][18][19][20][21]. Furthermore, in this big data era, many domains such as image processing, text categorization, biometric, microarray, etc.…”

Section: Related Workmentioning

confidence: 99%

“…Under such conditions, approximation task using available datasets can become a challenging task and difficult . This problem is more challenging in distance based learning algorithms such as RBFN [14,22,23], k-nearest neighbor [24][25], clustering method [21,[26][27][28][29] and support vector machine [30][31][32]. By default, the NN algorithm must search through all available training samples which requires large memory, and performs distance to center calculation, is slow during training of NN for approximation purposes.…”

Section: Related Workmentioning

confidence: 99%

Distance Weighted K-Means Algorithm for Center Selection in Training Radial Basis Function Networks

Aik

Hong

Junoh

2019

IJ-AI

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The accuracies rates of the neural networks mainly depend on the selection of the correct data centers. The K-means algorithm is a widely used clustering algorithm in various disciplines for centers selection. However, the method is known for its sensitivity to initial centers selection. It suffers not only from a high dependency on the algorithm's initial centers selection but, also from data points. The performance of K-means has been enhanced from different perspectives, including centroid initialization problem over the years. Unfortunately, the solution does not provide a good trade-off between quality and efficiency of the centers produces by the algorithm. To solve this problem, a new method to find the initial centers and improve the sensitivity to the initial centers of K-means algorithm is proposed. This paper presented a training algorithm for the radial basis function network (RBFN) using improved K-means (KM) algorithm, which is the modified version of KM algorithm based on distance-weighted adjustment for each centers, known as distance-weighted K-means (DWKM) algorithm. The proposed training algorithm, which uses DWKM algorithm select centers for training RBFN obtained better accuracy in predictions and reduced network architecture compared to the standard RBFN. The proposed training algorithm was implemented in MATLAB environment; hence, the new network was undergoing a hybrid learning process. The network called DWKM-RBFN was tested against the standard RBFN in predictions. The experimental models were tested on four literatures nonlinear function and four real-world application problems, particularly in Air pollutant problem, Biochemical Oxygen Demand (BOD) problem, Phytoplankton problem, and forex pair EURUSD. The results are compared to proposed method for root mean square error (RMSE) in radial basis function network (RBFN). The proposed method yielded a promising result with an average improvement percentage more than 50 percent in RMSE.

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“…Radial basis function networks (RBFN) are well-known for its ability to generalize and approximate a sample data without the requirement for the equation and coefficients, particularly when an unknown model describing an unknown complex relation with abundant training data. Due to their ability to generalize substantially, RBFN are usually selected for this purpose [11][12][13][14][15][16][17][18][19][20][21][22][23]. Furthermore, in this big data era, many domains such as image processing, text categorization, biometric, microarray, etc.…”

Section: Related Workmentioning

confidence: 99%

“…RBFN were reported has an extensive applications and its algorithms have many different variants [11,19,66,67]. Yeh and Chen [68] proposed an improved RBFN with kernel shape parameters to derive its learning rules in supervised learning, which is superior to conventional RBFN.…”

Section: Improved Rbfn (Irbfn)mentioning

confidence: 99%

An Improved Radial Basis Function Networks in Networks Weights Adjustment for Training Real-World Nonlinear Datasets

Aik

Hong

Junoh

2019

IJ-AI

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In neural networks, the accuracies of its networks are mainly relying on two important factors which are the centers and the networks weight. The gradient descent algorithm is a widely used weight adjustment algorithm in most of neural networks training algorithm. However, the method is known for its weakness for easily trap in local minima. It suffers from a random weight generated for the networks during initial stage of training at input layer to hidden layer networks. The performance of radial basis function networks (RBFN) has been improved from different perspectives, including centroid initialization problem to weight correction stage over the years. Unfortunately, the solution does not provide a good trade-off between quality and efficiency of the weight produces by the algorithm. To solve this problem, an improved gradient descent algorithm for finding initial weight and improve the overall networks weight is proposed. This improved version algorithm is incorporated into RBFN training algorithm for updating weight. Hence, this paper presented an improved RBFN in term of algorithm for improving the weight adjustment in RBFN during training process. The proposed training algorithm, which uses improved gradient descent algorithm for weight adjustment for training RBFN, obtained significant improvement in predictions compared to the standard RBFN. The proposed training algorithm was implemented in MATLAB environment. The proposed improved network called IRBFN was tested against the standard RBFN in predictions. The experimental models were tested on four literatures nonlinear function and four real-world application problems, particularly in Air pollutant problem, Biochemical Oxygen Demand (BOD) problem, Phytoplankton problem, and forex pair EURUSD. The results are compared to IRBFN for root mean square error (RMSE) values with standard RBFN. The IRBFN yielded a promising result with an average improvement percentage more than 40 percent in RMSE.

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Vector field radial basis function approximation

Cited by 18 publications

References 27 publications

Efficient Speed-Up of Radial Basis Functions Approximation and Interpolation Formula Evaluation

Efficient Speed-Up of Radial Basis Functions Approximation and Interpolation Formula Evaluation

Distance Weighted K-Means Algorithm for Center Selection in Training Radial Basis Function Networks

An Improved Radial Basis Function Networks in Networks Weights Adjustment for Training Real-World Nonlinear Datasets

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