• The Pure and Applied Mathematics
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• v.11 no.2
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• pp.103-115
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• 2004

A computational algorithm is developed for fitting given data in the plane or in 3-space by implicitly defined quadrics. Implicity implies that the type of the quadric is part of the model and need not be known in advance. Starting with some estimate for the coefficients of the quadric the method will alternatively determine the shortest distances from the given points onto the quadric and adapt the coefficients such as to reduce the sum of those squared distances. Numerical examples are given.

• Korean Journal of Computational Design and Engineering
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• v.17 no.4
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• pp.282-293
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• 2012

This paper presents an error-bounded B-spline fitting technique to approximate unorganized data within a prescribed error tolerance. The proposed approach includes two main steps: leastsquares minimization and error-bounded approximation. A B-spline hypervolume is first described as a data representation model, which includes its mathematical definition and the data structure for implementation. Then we present the least-squares minimization technique for the generation of an approximate B-spline model from the given data set, which provides a unique solution to the problem: overdetermined, underdetermined, or ill-conditioned problem. We also explain an algorithm for the error-bounded approximation which recursively refines the initial base model obtained from the least-squares minimization until the Euclidean distance between the model and the given data is within the given error tolerance. The proposed approach is demonstrated with some examples to show its usefulness and a good possibility for various applications.

• Smart Media Journal
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• v.3 no.2
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• pp.9-13
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• 2014

The Levenberg-Marquardt (LM) algorithm is the most widely used fitting algorithm. It outperforms simple gradient descent and other conjugate gradient methods in a wide variety of problems. Based on the work of paper[1], we propose a modified Levenberg-Marquardt algorithm for better performance of mobile system. The LM parameter at the $k_{th}$ iteration is chosen ${\mu}=A{\bullet}{\parallel}f(x){\parallel}{\bullet}I$ where f is the residual function, and J is the Jacobi of f. In this paper, we show this method is more efficient than traditional method under the situation that the system iteration is limited.

• Korean Journal of Computational Design and Engineering
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• v.12 no.1
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• pp.27-38
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• 2007

This paper describes a multiresidual approximation method for scattered volumetric data modeling. The approximation method employs a volumetric NURBS or VNURBS as a data interpolating function and proposes two multiresidual methods as a data modeling algorithm. One is called as the residual series method that constructs a sequence of VNURBS functions and their algebraic summation produces the desired approximation. The other is the residual merging method that merges all the VNURBS functions mentioned above into one equivalent function. The first one is designed to construct wavelet-type multiresolution models and also to achieve more accurate approximation. And the second is focused on its improvement of computational performance with the save fitting accuracy for more practical applications. The performance results of numerical examples demonstrate the usefulness of VNURBS approximation and the effectiveness of multiresidual methods. In addition, several graphical examples suggest that the VNURBS approximation is applicable to various applications such as surface modeling and fitting problems.

• International Journal of Highway Engineering
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• v.20 no.2
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• pp.57-65
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• 2018

PURPOSES : The study aims to predict the service life of national highway asphalt pavements through deep learning methods by using maintenance history data of the National Highway Pavement Management System. METHODS : For the configuration of a deep learning network, this study used Tensorflow 1.5, an open source program which has excellent usability among deep learning frameworks. For the analysis, nine variables of cumulative annual average daily traffic, cumulative equivalent single axle loads, maintenance layer, surface, base, subbase, anti-frost layer, structural number of pavement, and region were selected as input data, while service life was chosen to construct the input layer and output layers as output data. Additionally, for scenario analysis, in this study, a model was formed with four different numbers of 1, 2, 4, and 8 hidden layers and a simulation analysis was performed according to the applicability of the over fitting resolution algorithm. RESULTS : The results of the analysis have shown that regardless of the number of hidden layers, when an over fitting resolution algorithm, such as dropout, is applied, the prediction capability is improved as the coefficient of determination ($R^2$) of the test data increases. Furthermore, the result of the sensitivity analysis of the applicability of region variables demonstrates that estimating service life requires sufficient consideration of regional characteristics as $R^2$ had a maximum of between 0.73 and 0.84, when regional variables where taken into consideration. CONCLUSIONS : As a result, this study proposes that it is possible to precisely predict the service life of national highway pavement sections with the consideration of traffic, pavement thickness, and regional factors and concludes that the use of the prediction of service life is fundamental data in decision making within pavement management systems.

• Journal of the Korean Data and Information Science Society
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• v.18 no.4
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• pp.847-857
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• 2007

This paper provides a statistical algorithm which detects COD (chemical oxygen demand) measurement machine error on real-time. For this we propose to use regression model fitting and check its validity against the current observations. The main idea is that the normal regression relation between COD measurement and other parameters inside the machine will be violated when the machine is out of order.

• The Korean Journal of Applied Statistics
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• v.29 no.3
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• pp.513-523
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• 2016

Fitting a mixture of multivariate skew normal distribution (MSNMix) with multiple skewness parameter vectors via EM algorithm often requires a highly expensive computational cost to calculate the moments and probabilities of multivariate truncated normal distribution in E-step. Subsequently, it is common to fit an asymmetric data set with MSNMix with a simple skewness parameter vector since it allows us to compute them in E-step in an univariate manner that guarantees a cheap computational cost. However, the adaptation of a simple skewness parameter is unrealistic in many situations. This paper proposes an approximate estimation for the MSNMix with multiple skewness parameter vectors that also allows us to treat them in an univariate manner. We additionally provide some experiments to show its effectiveness.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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• pp.404-409
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• 1998

In this paper, we propose a learning algorithm of fuzzy neural networks with trapezoidal fuzzy weights. This fuzzy neural networks can use fuzzy numbers as well as real numbers, and represent linguistic information better than standard neural networks. We construct trapezodal fuzzy weights by the composition of two triangles, and devise a learning algorithm using the two triangular membership functions, The results of computer simulations on numerical data show that the fuzzy neural networks have high fitting ability for target output.

• Proceedings of the IEEK Conference
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• 2002.06c
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• pp.203-206
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• 2002

We propose the new algorithm for scene segmentation. The proposed system consists motion estimation module and motion segmentation module. The former estimates 2D-motion value for each pixel position from two images transformed by wavelet. The latter determine scene segments well fitting on dominant affine motion models. What distinguishes proposed algorithm from other methods is that it needs not other post-processing for scene segmentation. We can manipulate both multimedia data and objects in virtual environment using proposed algorithm.

• Korean Journal of Computational Design and Engineering
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• v.10 no.3
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• pp.162-167
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• 2005

A 3D solid element mesh generation algorithm was newly developed. 3D surface points of global rectangular coordinates were supplied by a 3D laser scanner. The algorithm is strait forward and simple but it generates hexahedral solid elements. Then, the surface rectangular elements were generated from the solid elements. The key of the algorithm is elimination of unnecessary elements and 3D boundary surface fitting using given 3D surface point data.