• Journal of the Korea Society of Computer and Information
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• v.14 no.8
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• pp.11-18
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• 2009

This paper proposes the way of improving learning speed in Levenberg-Marquardt algorithm using the principal submatrix of Jacobian matrix. The Levenberg-Marquardt learning uses Jacobian matrix for Hessian matrix to get the second derivative of an error function. To make the Jacobian matrix an invertible matrix. the Levenberg-Marquardt learning must increase or decrease ${\mu}$ and recalculate the inverse matrix of the Jacobian matrix due to these changes of ${\mu}$. Therefore, to have the proper ${\mu}$, we create the principal submatrix of Jacobian matrix and set the ${\mu}$ as the eigenvalues sum of the principal submatrix. which can make learning speed improve without calculating an additional inverse matrix. We also showed that our method was able to improve learning speed in both a generalized XOR problem and a handwritten digit recognition problem.

• Journal of the Korean Data and Information Science Society
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• v.23 no.5
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• pp.1027-1035
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• 2012

This paper proposes a new Levenberg-Marquardt algorithm that is accelerated by adjusting a Jacobian matrix and a quasi-Hessian matrix. The proposed method partitions the Jacobian matrix into block matrices and employs the inverse of a partitioned matrix to find the inverse of the quasi-Hessian matrix. Our method can avoid expensive operations and save memory in calculating the inverse of the quasi-Hessian matrix. It can shorten the training time for fast convergence. In our results tested in a large application, we were able to save about 20% of the training time than other algorithms.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.14 no.8
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• pp.803-808
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• 2003

Several dielectric pipes buried in the lossy half space are reconstructed from the scattered fields measured along the interface between the air and the lossy ground. Iterative inversion method by using the hybrid optimization algorithm combining the genetic and the Levenberg-Marquardt algorithm enables us to find the positions, the sizes, and the medium parameters such as the permittivities and the conductivities of the buried pipes as well as those of the background lossy half space even when the dielectric pipes are close together. Illposedness of the inversion caused by the errors in the measured scattered fields are regularized by filtering the evanescent modes of the scattered fields out.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.8 no.5
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• pp.534-544
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• 1997

The permittivity distribution of a two-dimensional high-contrast object with large size, which leads to the global minimum of cost function, is reconstructed by iteratively using the hybrid algorithm of Levenberg-magquardt algorithm(LMA) plus Genetic Algorithm(GA). The scattered fields calculated in a cost function are expanded in angular spectral modes, of which only effective propagating modes are used. The definition of cost function based on the effective propagating modes enables us to formulate the minimum number of incident waves for the reconstruction of object. It is numerically shown that LMA has an advantage of fast convergence but can't reconstruct a high-contrast object with large size and GA can reconstruct a high-contrast object with large size but has an disadvantage of slow convergence, whereas an inverse scattering technique using the hybrid algorithm adopts only advantages of LMA and GA.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.22 no.12
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• pp.1124-1131
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• 2011

In this paper, image reconstruction algorithm for breast cancer detection using MT(Microwave Tomography) was investigated. The breast cancer detection system under development uses 16 transmit/receive antennas. The signal waveform was a sinusoidal wave at 900 MHz. To solve the 2D inverse scattering problem, we used the 2D FDTD (Finite Difference Time Domain) method for forward calculation and LMA(Levenberg-Marquardt Algorithm) for optimization. The result of the image reconstruction using the numerical phantom by MRI(Magnetic Resonance Imaging) obtained from real patient of breast cancer showed that we can detect the position of the tumor accurately.

• Communications of the Korean Mathematical Society
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• v.16 no.3
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• pp.445-458
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• 2001

The shape and the distribution of material construction of the scatterer may be obtained from its scattered fields by the iterative inversion in the spectral domain. The illposedness, the resolution, and the uniqueness of the inversion are the key problems in the inversion and inter-related. The illposedness is shown to be caused by the evanescent modes which carries and amplifies exponentially the measurement errors in the back-propagation of the measured scattered fields. By filtering out all the evanescent modes in the cost functional defined as the squared difference between the measured and the calculated spatial spectrum of the scattered fields from the iteratively chosen medium parameters of the scatterer, one may regularize the illposedness of the inversion in the expense of the resolution. There exist many local minima of the cost functional for the inversion of the large and the high-contrast scatterer and the hybrid algorithm combining the genetic algorithm and the Levenberg-Marquardt algorithm is shown to find efficiently its global minimum. The resolution of reconstruction obtained by keeping all the propating modes and filtering out the evanescent modes for the regularization becomes 0.5 wavelength. The super resolution may be obtained by keeping the evanescent modes when the measurement error and instance, respectively, are small and near.

• Journal of the Earthquake Engineering Society of Korea
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• v.11 no.1 s.53
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• pp.89-97
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• 2007

Parameters including the seismic sources and the elastic wave propagation characteristics were analysed using the observed ground motions from 12 Fukuoka region earthquakes. The Levenberg-Marquardt algorithm was applied to invert all the variables non-linearly and simultaneously with S wave energy in fiequency domain. Average stress drop of 12 events and local attenuation parameter $\kappa$ under seismic stations were estimated to about 79.2-bar and 0.043 respectively. Regional attenuation parameter, Qo and ${\eta}$, were also estimated to be about 248.1 and 0.558 respectively. Low value of Qo seems to caused by inhomogeneous tectonic characteristics between Japan island and southern Korean peninsula. $\kappa$ values are much higher than that characterizing EUS (Eastern United States) region, and nearly similar to that of WUS (Western Waited States) region. If the informations on site specific amplification of all the seismic stations are known, $\kappa$ values can be estimated more precisely. All the values including the seismic sources and the site and crustal scale propagation characteristics can be used as seismic design parameters.

• Tunnel and Underground Space
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• v.20 no.2
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• pp.97-104
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• 2010

The materials failure relation $\ddot{\Omega}=A{(\dot{\Omega})}^\alpha$ where $\Omega$ is a measurable quantity such as displacement and the dot superscript is the time derivative, may be used to analyze the accelerating creep of materials. Coefficients, A and $\alpha$, are determined by fitting given data sets. In this study, it is tried to predict the failure time of tunnel using the materials failure relation. Four fitting techniques of applying the materials failure relation are attempted to forecast a failure time. Log velocity versus log acceleration technique, log time versus log velocity technique, inverse velocity technique are based on the linear least squares fits and non-linear least squares technique utilizes the Levenberg-Marquardt algorithm. Since the log velocity versus log acceleration technique utilizes a logarithmic representation of the materials failure relation, it indicates the suitability of the materials failure relation applied to predict a failure time of tunnel. A linear correlation between log velocity and log acceleration appears satisfactory(R=0.84) and this represents that the materials failure relation is a suitable model for predicting a failure time of tunnel. Through comparing the real failure time of tunnel with the predicted failure times from four curve fittings, it is shown that the log time versus log velocity technique results in the best prediction.