W. Kamiński, P. Strumiłło · IEEE Transactions on Neural Networks · 1997
This paper deals with optimization of the computations involved in training radial basis function (RBF) neural networks. The main contribution of the reported work is the method for network weights calculation, in which the key idea is to transform the RBF kernels into an orthonormal set of functions (using the standard Gram-Schmidt orthogonalization). This significantly reduces the computing time if the RBF training scheme, which relies on adding one kernel hidden node at a time to improve network performance, is adopted. Another property of the method is that, after the RBF network weights are computed, the original network structure can be restored back. An additional strength of the method is the possibility to decompose the proposed computing task into a number of parallel subtasks so gaining further savings on computing time. Also, the proposed weight calculation technique has low storage requirements. These features make the method very attractive for hardware implementation. The paper presents a detailed derivation of the proposed network weights calculation procedure and demonstrates its validity for RBF network training on a number of data classification and function approximation problems.
Cited by 104
Yuan Wang, Yunde Jia · 2008
Linear subspace analysis has been extensively applied to face recognition. However, a linear subspace can not describe the nonlinear variations of face images. Alternatively, a kernel feature space can reflect nonlinear information of faces. In this paper we present a new face recognition method based on Radial Basis Function (RBF) networks in kernel space. The face features are extracted in kernel space and then fed into an RBF network, resulting in a face recognition algorithm that is computationally simple and robust. The experimental results show that our algorithm performs better than a traditional RBF network for face recognition. 1
Cited by 0
I‐Cheng Yeh, Xinying Zhang, Chong Wu et al. · 2010
Radial basis function network (RBFN) which is commonly used in the classification problems has two parameters, a kernel center and a radius that can be determined by unsupervised or supervised learning. However, it has a disadvantage that it considers that all the independent variables have the equal weights. Thus the contour lines of the kernel function are circular, but in fact, the influence of each independent variable on the model is so different that more reasonable contour lines should be oval. To overcome this disadvantage, this paper presents an adaptive radial basis function network (ARBFN) with kernel shape parameters and derives the learning rules from supervised learning. The results show that ARBFN is much more accurate than the traditional RBFN, reflecting that the shape parameter can really improve the accuracy of RBFN.
Cited by 6
Xiaojian Zhou, Meng Zhang, Qi Cui et al. · Journal of Mathematical Analysis and Applications · 2025
Cited by 2
Lei Xu, Adam Krzyżak, Alan Yuille · 2003
After building up some connections between the radial basis function (RBF) network and kernel regression estimator (KRE), the authors introduce several recent theoretical results on KRE. They show that KRE can not only be used as a neural network model, but can also provide new results on the theoretical analysis of an RBF net in terms of the ability of approximation, the rate of convergence, and the size of the receptive field of the radial basis function. These results are quite useful for further theoretical studies on the RBF as well as in guiding the design of the RBF net in practice.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
Cited by 1
De Bie, Hendrik, De Martino, Antonino, Diki, Kamal · ArXiv.org · 2025
We introduce a polyanalytic extension of the Gaussian radial basis function (RBF) kernel by computing the action of the convolution operator on normalized Hermite functions. In particular, using the Zaremba-Bergman formula we derive an explicit closed form for this new reproducing kernel function. We then establish an isomorphism relating the reproducing kernel Hilbert space induced by the polyanalytic Gaussian RBF kernel with the corresponding polyanalytic Fock space. Moreover, we provide a characterization of polyanalytic Gaussian RBF spaces in terms of a Landau-type operator. In addition, we investigate the polyanalytic counterpart of the Weyl operator, which leads to applications involving the Christoffel-Darboux formula for Hermite polynomials and Mehler's kernel. Finally, we discuss the analogue of the Weyl operator in the context of the polyanalytic Gaussian RBF setting.
Cited by 0Open access
M. Pawlak, Mark Ng · 2002
We describe alternative learning schemes for radial basis function (RBF) networks both in the context of classification and function recovering problems. The connection between RBF networks and well established kernel-type regression estimators is exhibited. We show that the asymptotic accuracy (convergence and rate of convergence) of the proposed RBF nets can be equivalent to the kernel technique.
Cited by 5
Glori Stephani Saragih, Sri Hartini, Zuherman Rustam · Bulletin of Miscellaneous Information (Royal Gardens Kew) · 2021
This paper compares the fuzzy kernel k-medoids using radial basis function (RBF) and polynomial kernel function in hepatitis classification. These two kernel functions were chosen due to their popularity in any kernel-based machine learning method for solving the classification task. The hepatitis dataset then used to evaluate the performance of both methods that were expected to provide an accurate diagnosis in patients to obtain treatment at an early phase. The data were obtained from two hospitals in Indonesia, consisting of 89 hepatitis-B and 31 hepatitis-C samples. The data were analyzed using several cases of k-fold cross-validation, and the performances were compared according to their accuracy, sensitivity, precision, F1-Score, and running time. From the experiments, it was concluded that fuzzy kernel k-medoids using RBF kernel function is better compared to polynomial kernel function with the 6% increment of accuracy, 13% enhancement of sensitivity, and 5% improvement in F1-Score. On the other side, the precision of fuzzy kernel k-medoids using polynomial kernel function is 2% higher than using the RBF kernel function. According to the results, the use of RBF or polynomial kernel function in fuzzy kernel medoids can be considered according to the primary goal of the classification.
Cited by 0Open access
Saeid Niazmardi · arXiv (Cornell University) · 2024
Kernel-based classification methods, particularly the support vector machine (SVM), are among the most common algorithms for hyperspectral data classification. The Radial Basis function (RBF) kernel has earned great popularity in hyperspectral data classification due to its superior performance among other available kernel functions. Nonetheless, the cross-validation technique usually used for tunning the RBF parameter can be time-consuming and may result in sub-optimal values for the parameter. This paper proposed the cluster-based random radial basis function (CRRBF) kernel function as an alternative to the RBF kernel to achieve similar performance with a more manageable parameter, which is the number of clusters. The CRRBF kernel initially clusters the hyperspectral bands and then constructs an RBF kernel with a randomly assigned value as the kernel parameter from each cluster of bands. The final CRRBF kernel is constructed by adding up these basis RBF kernels. We have designed several experiments to evaluate the SVM performance trained with the CRRBF kernel considering a different number of clusters and training samples, using three hyperspectral data sets. The obtained results showed that the CRRBF kernel could provide comparable or better results than the RBF. The results also showed that the classification performance is pretty robust to the number of clusters, as the only open parameter of the CRRBF kernel.
Cited by 0Open access
Nabil Benoudjit, Michel Verleysen · 2003
Abstract. RBFN (Radial-Basis Function Networks) represent an attractive alternative to other neural network models. Their learning is usually split into an unsupervised part, where center and widths of the basis functions are set, and a linear supervised part for weight computation. Although available literature on RBFN learning widely covers how basis function centers and weights must be set, little effort has been devoted to the learning of basis function widths. This paper addresses this topic: it shows the importance of a proper choice of basis function widths, and how inadequate values can dramatically influence the approximation performances of the RBFN. It also suggests a one-dimensional searching procedure as a compromise between an exhaustive search on all basis function widths, and a non-optimal a priori choice.
Cited by 0
Yangguang Liu, Xiaoqi He, Bin Xu · 2010
In order to reduce computer storage requirements for kernel matrix and the computational costs for floating point operations in kernel machine learning, compactly supported radial basis function is used for kernel machine to construct sparse kernel matrix. This paper deals with evaluation and comparison of compactly supported radial basis function for kernel machine in three aspects: the savings in storage, computation time for training, and performance. It is shown that savings in storage can be adjusted by user parameters, computation time for training decreases but it doest not mean that the more sparse the less training time, it will be stationary when ratio of non-zero elements of kernel matrix is in some range, the test accuracy to evaluate performance do not change much from our experimental results.
Cited by 1
Antonius Ricky, Kennedy Genesius, Michelle Setiawan et al. · 2022
Currently, one of the most popular types of investment by the Indonesian people is stocks. This is evidenced by data from the Indonesia Stock Exchange, until the end of 2020, the number of capital market investors increased 56% from 2019 to 3.88 million investors. The purpose of this study is to increase public interest, especially the millennial generation, to invest in stocks, to increase profits from investing in stocks, and to reduce suicides due to losses from investing in stocks. In addition, the method used in this study is the Support Vector Regressor. From this research, the results of the Support Vector Regressor Train results for Root Mean Square Error are 179.17, R2 are 1.0, and Mean Absolute Error are 1.48 while the Support Vector Regressor Test results for Root Mean Square Error are 228.79, R2 are 0.99, and Mean Absolute Error are 13.80. Therefore, the Support Vector Regressor model is suitable for predicting stock prices.
Cited by 2
Mohd Zulfaezal Che Azemin, Mohd Radzi Hilmi, Khairidzan Mohd Kamal et al. · 2014
Information obtained from redness grading can assist clinician for diagnosis and in making clinical decision. This research work aims to mimic human perception of fibrovascular redness using features extracted from color entropy. Gaussian process regression with the radial basis function kernel has been employed to fuse relevant features and established the model of redness perception. In this paper, we present the results of the radial basis function kernel incorporated as the covariance function in the GPR as the scale, sigma is varied.
Cited by 15
Zhihua Ye, Honglian Li · 2012
Support Vector Machine (SVM) is a new statistical learning method, as a speaker recognition method it has unique advantages. In speaker recognition, the selection of kernel function is a key factor to decide SVM's performance. Among them, Radial Basis Function (RBF) kernel function is the widely used kernel function, and it has two parameters: the punishment factor C and kernel parameters kernelpar. In this paper the parameters (C, kernelpar) of the RBF kernel function are adjusted to find the optimal parameters. It can be seen from the research that the time-consuming and recognition rate can both affect the selection of the optimal parameters.
Cited by 11
Chooleewan Dachapak, Shunshoku Kanae, Zi-Jiang Yang et al. · IFAC Proceedings Volumes · 2004
Cited by 2
Yang Zhao, Siming Zheng, Jihong Pei et al. · Information Sciences · 2024
Cited by 1
Michael Botsch, Josef A. Nossek · 2008
In many practical applications besides a small generalization error also the interpretability of classification systems is of great importance. There is always a tradeoff among these two properties of classifiers. The similarity measure in the input space as defined by one of the most powerful classifiers, the Random Forest (RF) algorithm, is used in this paper as basis for the construction of Generalized Radial Basis Function (GRBF) classifiers. Hereby, interpretability and a low generalization error can be achieved. The main idea is to approximate the RF kernel by Gaussian functions in a GRBF network. This way the GRBF network can be constructed to approximate the conditional probability of each class given a query input. Since each center in the GRBF is used for the representation of the distribution of a single target class in a localized area of the classifiers input space, interpretability can be achieved by taking account for the membership of a query input to the different localized areas. Whereas in most algorithms the pruning technique is used only to improve the generalization property, here a method is proposed how pruning can be applied to additionally improve the interpretability. Another benefit that comes along with the resulting GRBF classifier is the possibility to detect outliers and to reject decisions that have a low confidence. Experimental results underline the advantages of the classification system.
Cited by 8
Yang Zhao, Jihong Pei, Hao Chen · Applied Soft Computing · 2019
Cited by 30
Adyatma Bhaskara Hutomo · 2014
ADYATMA BHASKARA HUTOMO. News Document Classification Using Support Vector Machine Method with Radial Basis Function Kernel. Supervised by JULIO ADISANTOSO. Every day the number of text documents, especially online news documents increase. As a result, it is more difficult for information seekers in obtaining the desired information. This problem requires a text processing technique that is able to automatically classify text documents based on predetermined categories. This technique is document classification. A very good and popular classification method is support vector machine (SVM). SVM tries to find the best hyperplane which separates 2 classes of data in a vector space. By applying kernel trick, SVM can implement classification in non-linear case. The goals of this research are applying the radial basis function kernel of SVM to classify Reuters-21578 news documents, and comparing the weighting method term frequency (tf) and term frequency-inverse document frequency (tf-idf). The research uses chi-square in feature selection, producing 1716 features out of 7279 terms from tokenization and stopwords removal. The final result shows that the SVM classification produces an accuracy of 93.21% using tf weighting and 92.97% using tf-idf weighting.
Cited by 1
Nur Suhaili Mansor, Hapini Awang, Sarkin Tudu Shehu Malami et al. · Communications in computer and information science · 2024
Cited by 6