• Journal of applied mathematics & informatics
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• v.38 no.5_6
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• pp.519-532
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• 2020

In this paper, we first propose a new total variation-based regularization model for image restoration. We next propose a fixed-point-like method for solving the new image restoration model, and then we provide convergence analysis for the fixed-point-like method. To evaluate the feasibility and efficiency of the fixed-point-like method for the new proposed total variation-based regularization model, we provide numerical experiments for several test problems.

• Journal of the Korean Mathematical Society
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• v.54 no.6
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• pp.1905-1926
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• 2017

In this paper we introduce a new iterative method by the combination of the prox-Tikhonov regularization and the alternating resolvents for finding a common zero of two accretive operators in Banach spaces. And we will give some applications and numerical examples. The results of this paper improve and extend the corresponding results announced by many others.

• Communications for Statistical Applications and Methods
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• v.18 no.6
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• pp.733-739
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• 2011

The linear absolute shrinkage and selection operator(Lasso) method improves the low prediction accuracy and poor interpretation of the ordinary least squares(OLS) estimate through the use of $L_1$ regularization on the regression coefficients. However, the Lasso is not robust to outliers, because the Lasso method minimizes the sum of squared residual errors. Even though the least absolute deviation(LAD) estimator is an alternative to the OLS estimate, it is sensitive to leverage points. We propose a robust Lasso estimator that is not sensitive to outliers, heavy-tailed errors or leverage points.

• Genomics & Informatics
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• v.14 no.4
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• pp.187-195
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• 2016

In genetic association studies with high-dimensional genomic data, multiple group testing procedures are often required in order to identify disease/trait-related genes or genetic regions, where multiple genetic sites or variants are located within the same gene or genetic region. However, statistical testing procedures based on an individual test suffer from multiple testing issues such as the control of family-wise error rate and dependent tests. Moreover, detecting only a few of genes associated with a phenotype outcome among tens of thousands of genes is of main interest in genetic association studies. In this reason regularization procedures, where a phenotype outcome regresses on all genomic markers and then regression coefficients are estimated based on a penalized likelihood, have been considered as a good alternative approach to analysis of high-dimensional genomic data. But, selection performance of regularization procedures has been rarely compared with that of statistical group testing procedures. In this article, we performed extensive simulation studies where commonly used group testing procedures such as principal component analysis, Hotelling's $T^2$ test, and permutation test are compared with group lasso (least absolute selection and shrinkage operator) in terms of true positive selection. Also, we applied all methods considered in simulation studies to identify genes associated with ovarian cancer from over 20,000 genetic sites generated from Illumina Infinium HumanMethylation27K Beadchip. We found a big discrepancy of selected genes between multiple group testing procedures and group lasso.

• Structural Monitoring and Maintenance
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• v.6 no.3
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• pp.219-235
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• 2019

Scheduled inspections of common crossings are one of the main cost drivers of railway maintenance. Prognostics and health management (PHM) approach and modern monitoring means offer many possibilities in the optimization of inspections and maintenance. The present paper deals with data driven prognosis of the common crossing remaining useful life (RUL) that is based on an inertial monitoring system. The problem of scheduled inspections system for common crossings is outlined and analysed. The proposed analysis of inertial signals with the maximal overlap discrete wavelet packet transform (MODWPT) and Shannon entropy (SE) estimates enable to extract the spectral features. The relevant features for the acceleration components are selected with application of Lasso (Least absolute shrinkage and selection operator) regularization. The features are fused with time domain information about the longitudinal position of wheels impact and train velocities by multivariate regression. The fused structural health (SH) indicator has a significant correlation to the lifetime of crossing. The RUL prognosis is performed on the linear degradation stochastic model with recursive Bayesian update. Prognosis testing metrics show the promising results for common crossing inspection scheduling improvement.

• Journal of the Korean Data and Information Science Society
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• v.28 no.6
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• pp.1229-1244
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• 2017

In recent years, as demand for data-based analytical methodologies increases in various fields, optimization methods have been developed to handle them. In particular, various constraints required for problems in statistics and machine learning can be solved by convex optimization. Alternating direction method of multipliers (ADMM) can effectively deal with linear constraints, and it can be effectively used as a parallel optimization algorithm. ADMM is an approximation algorithm that solves complex original problems by dividing and combining the partial problems that are easier to optimize than original problems. It is useful for optimizing non-smooth or composite objective functions. It is widely used in statistical and machine learning because it can systematically construct algorithms based on dual theory and proximal operator. In this paper, we will examine applications of ADMM algorithm in various fields related to statistics, and focus on two major points: (1) splitting strategy of objective function, and (2) role of the proximal operator in explaining the Lagrangian method and its dual problem. In this case, we introduce methodologies that utilize regularization. Simulation results are presented to demonstrate effectiveness of the lasso.

• Proceedings of the Korea Society for Industrial Systems Conference
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• 2001.05a
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• pp.247-251
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• 2001

영상을 처리하는 과정에서 광학시스템과 전기시스템의 특성으로 인해 흐려지고 잡음으로 훼손된 영상을 복원하는 경우에 일반적으로 정칙화 반복복원방법이 사용된다. 기존의 방법은 영상의 국부적인 특성을 고려하지 않고 영상전체에 일률적으로 정칙화 연산자를 사용함으로써 윤곽부분에서는 리플잡음을 초래하고 평면부분에서도 잡음증폭을 피할 수 없으며, 또한 시각적으로 효율적이지 못한 면이 있다. 본 논문에서는 이러한 문제점을 개선하기 위하여, 영상의 국부적인 특성을 고려하여 적응 정칙화 파라메타와 적응 정칙화 연산지를 사용하여 평면영역과 윤곽영역의 방향특성에 따라 적응적으로 처리하는 반복복원방법을 제안한다. 제안한 방법은 기존의 방법과 비교하여 평면영역에서의 잡음 평활화가 개선되고 시각적으로 중요한 윤곽부분 복원에 효율적임을 실험결과를 통해 알 수 있었으며 ISNR 면에서도 우수하였다.

• Nuclear Engineering and Technology
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• v.37 no.2
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• pp.127-138
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• 2005

Approaches to several recent issues in the operation of nuclear power plants using computational intelligence are discussed. These issues include 1) noise analysis techniques, 2) on-line monitoring and sensor validation, 3) regularization of ill-posed surveillance and diagnostic measurements, 4) transient identification, 5) artificial intelligence-based core monitoring and diagnostic system, 6) continuous efficiency improvement of nuclear power plants, and 7) autonomous anticipatory control and intelligent-agents. Several changes to the focus of Computational Intelligence in Nuclear Engineering have occurred in the past few years. With earlier activities focusing on the development of condition monitoring and diagnostic techniques for current nuclear power plants, recent activities have focused on the implementation of those methods and the development of methods for next generation plants and space reactors. These advanced techniques are expected to become increasingly important as current generation nuclear power plants have their licenses extended to 60 years and next generation reactors are being designed to operate for extended fuel cycles (up to 25 years), with less operator oversight, and especially for nuclear plants operating in severe environments such as space or ice-bound locations.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.37 no.3
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• pp.98-109
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• 2000

While the bispectrum has desirable properties in itself and therefore has a lot of potential to be applied to signal and Image restoration. few real-world application results have appeared in literature The major problem with this IS the difficulty In realizing the expectation operator of the true bispectrum, due to the lack of realizations. In this paper, the true bispectrum is defined as the expectation of the sample bispectrum, which IS the Fourier representation of the triple correlation given one realization The characteristics of the sample bispectrum are analyzed and a way to obtain an estimate of the true bispectrum without stochastic expectation, using the generalized theory of weighted regularization is shown. The bispectrum estimated by the proposed algorithm is experimentally demonstrated to be useful for signal recovery under blurred noisy condition.

• Communications for Statistical Applications and Methods
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• v.25 no.2
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• pp.235-243
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• 2018

Many studies exist on the influence of one or few observations on estimators in a variety of statistical models under the "large n, small p" setup; however, diagnostic issues in the regression models have been rarely studied in a high dimensional setup. In the high dimensional data, the influence of observations is more serious because the sample size n is significantly less than the number variables p. Here, we investigate the influence of observations on the least absolute shrinkage and selection operator (LASSO) estimates, suggested by Tibshirani (Journal of the Royal Statistical Society, Series B, 73, 273-282, 1996), and the influence of observations on selected variables by the LASSO in the high dimensional setup. We also derived an analytic expression for the influence of the k observation on LASSO estimates in simple linear regression. Numerical studies based on artificial data and real data are done for illustration. Numerical results showed that the influence of observations on the LASSO estimates and the selected variables by the LASSO in the high dimensional setup is more severe than that in the usual "large n, small p" setup.