• The Transactions of the Korean Institute of Electrical Engineers
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• v.45 no.4
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• pp.602-611
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• 1996

In this paper, radial basis function networks with two hidden layers, which employ the K-means clustering method and the hierarchical training, are proposed for improving the short-term predictability of chaotic time series. Furthermore the recursive training method of radial basis function network using the recursive modified Gram-Schmidt algorithm is proposed for the purpose. In addition, the radial basis function networks trained by the proposed training methods are compared with the X.D. He A Lapedes's model and the radial basis function network by nonrecursive training method. Through this comparison, an improved radial basis function network for predicting chaotic time series is presented. (author). 17 refs., 8 figs., 3 tabs.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.95-104
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• 2007

We study stationary subdivision schemes based on radial basis function interpolation. Each scheme has a tension parameter, say ${\lambda}$, which actually belongs to the radial basis function. In particular, adapted subdivision rules on bounded intervals are developed.

• Bulletin of the Korean Mathematical Society
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• v.51 no.2
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• pp.531-538
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• 2014

Concentric hyperspheres in the n-dimensional Euclidean space $\mathbb{R}^n$ are the level hypersurfaces of a radial function f : $\mathbb{R}^n{\rightarrow}\mathbb{R}$. The magnitude $||{\nabla}f||$ of the gradient of such a radial function f : $\mathbb{R}^n{\rightarrow}\mathbb{R}$ is a function of the function f. We are interested in the converse problem. As a result, we show that if the magnitude of the gradient of a function f : $\mathbb{R}^n{\rightarrow}\mathbb{R}$ with isolated critical points is a function of f itself, then f is either a radial function or a function of a linear function. That is, the level hypersurfaces are either concentric hyperspheres or parallel hyperplanes. As a corollary, we see that if the magnitude of a conservative vector field with isolated singularities on $\mathbb{R}^n$ is a function of its scalar potential, then either it is a central vector field or it has constant direction.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.58 no.6
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• pp.1223-1229
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• 2009

The performance of Radial Basis Function Neural Networks depends on setting up the Radial Basis Functions over the input space which are the important design procedure of Radial Basis Function Neural Networks. The existing method to initialize the location of the radial basis functions over the input space is to use the conditional fuzzy C-means clustering. However, the researchers which are interested in the conditional fuzzy C-means clustering cannot get as good modeling performance as they expect because the conditional fuzzy C-means clustering cannot project the information which is extracted over the output space into the input space. To compensate the above mentioned drawback of the conditional fuzzy C-means clustering, we apply a fuzzy K-nearest neighbors approach to project the auxiliary information defined over the output space into the input space without lose of the information.

• Clinics in Shoulder and Elbow
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• v.23 no.3
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• pp.131-135
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• 2020

Background: Resection of the radial head is a surgical indication for comminuted radial head fracture in which internal fixation is inaccessible. Some complications from the surgery can alter the function of the patient's elbow. The objective of this study was to assess functional outcome of the elbow after resection of the radial head. Methods: A retrospective longitudinal study was performed with patients who underwent radial head resection between 2008 and 2018. Elbow function was assessed by the Mayo Elbow Performance Index (MEPI) for 11 patients comprising three women and eight men. The mean follow-up was 47.6 months. The mean age was 41±10.3 years. Results: Nine patients had a stable and painless elbow. The mean extension-flexion arc was 97.73°±16.03°. The mean values of pronation and supination were 76.8° and 74.5°, respectively. The mean MEPI score was 83.2 points, and restoration of overall function was achieved in 81% of the cases. Poor function was noted in one in 10 that presented with a terrible triad. Conclusions: Resection of the radial head restored elbow functionality at a rate of 81%, which was a good outcome for patients.

• Publications of The Korean Astronomical Society
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• v.22 no.2
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• pp.35-41
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• 2007

We present the result of radial velocity observation of a W UMa type binary star EX Leo. We observed the star on February 16, 2003, using Long-Slit spectrograph of BOAO(Bohyunsan Optical Astronomical Observatory). Since the spectral lines are broad due to its fast rotation, it is difficult to distinguish two radial velocities from cross correlation function. Instead of cross correlation function, we used broadening function to develop our own code which estimate the radial velocity of the broadened line spectra. With our own code, radial velocities of primary and secondary stars are derived simultaneously. From the radial velocity curve fit, we obtained $K_1=50.24{\pm}8.29km/s$ and $K_2=254.05{\pm}20.984km/s$ respectively.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.435-443
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• 2007

An important approach towards solving the scattered data problem is by using radial basis functions. However, for a large class of smooth basis functions such as Gaussians, the existing theories guarantee the interpolant to approximate well only for a very small class of very smooth approximate which is the so-called 'native' space. The approximands f need to be extremely smooth. Hence, the purpose of this paper is to study approximation by a scattered shifts of a radial basis functions. We provide error estimates on larger spaces, especially on the homogeneous Sobolev spaces.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1087-1095
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• 2009

In this paper, we study approximation method from scattered data to the derivatives of a function f by a radial basis function $\phi$. For a given function f, we define a nearly interpolating function and discuss its accuracy. In particular, we are interested in using smooth functions $\phi$ which are (conditionally) positive definite. We estimate accuracy of approximation for the Sobolev space while the classical radial basis function interpolation applies to the so-called native space. We observe that our approximant provides spectral convergence order, as the density of the given data is getting smaller.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2000.11a
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• pp.459-462
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• 2000

In this paper, we propose the initial optimized structure of the Radial Basis Function Network which is more simple in the part of the structure and converges more faster than Neural Network with the analysis method using Time-Frequency Localization. When we construct the hidden node with the Radial Basis Function whose localization is similar with an approximation target function in the plane of the Time and Frequency, we make a good decision of the initial structure having an ability of approximation.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.61 no.1
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• pp.135-142
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• 2012

In this paper, we proposed a new architecture called radial basis function-based polynomial neural networks classifier that consists of heterogeneous neural networks such as radial basis function neural networks and polynomial neural networks. The underlying architecture of the proposed model equals to polynomial neural networks(PNNs) while polynomial neurons in PNNs are composed of Fuzzy-c means-based radial basis function neural networks(FCM-based RBFNNs) instead of the conventional polynomial function. We consider PNNs to find the optimal local models and use RBFNNs to cover the high dimensionality problems. Also, in the hidden layer of RBFNNs, FCM algorithm is used to produce some clusters based on the similarity of given dataset. The proposed model depends on some parameters such as the number of input variables in PNNs, the number of clusters and fuzzification coefficient in FCM and polynomial type in RBFNNs. A multiobjective particle swarm optimization using crowding distance (MoPSO-CD) is exploited in order to carry out both structural and parametric optimization of the proposed networks. MoPSO is introduced for not only the performance of model but also complexity and interpretability. The usefulness of the proposed model as a classifier is evaluated with the aid of some benchmark datasets such as iris and liver.