• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제2권2호
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• pp.81-95
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• 1998

The superconvergence of the Sloan iterate obtained from a Galerkin method for the approximate solution of the singular integral equation based on the use of two sets of orthogonal polynomials is investigated. The discrete Sloan iterate using Gaussian quadrature to evaluate the integrals in the equation becomes the Nystr$\ddot{o}$m approximation obtained by the same rules. Consequently, it is impossible to expect the faster convergence of the Sloan iterate than the discrete Galerkin approximation in practice.

• Journal of the Korean Data and Information Science Society
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• 제21권3호
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• pp.561-567
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• 2010

Multiclassification is typically performed using voting scheme methods based on combining a set of binary classifications. In this paper we use multiclassification method with a hat matrix of least squares support vector machine (LS-SVM), which can be regarded as the revised one-against-all method. To tackle multiclass problems for large data, we use the $Nystr\ddot{o}m$ approximation and the quadratic Renyi entropy with estimation in the primal space such as used in xed size LS-SVM. For the selection of hyperparameters, generalized cross validation techniques are employed. Experimental results are then presented to indicate the performance of the proposed procedure.

• 전자공학회논문지
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• 제52권2호
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• pp.162-170
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• 2015

컴뮤트 타임 임베딩을 구현하려면 그래프 라플라시안 행렬의 고유값과 고유벡터를 구하여야 하는데, $o(n^3)$의 계산량이 요구되어 대용량 데이터에는 적용하기 어려운 문제가 있다. 이를 줄이기 위하여 표본화 과정을 통하여 크기가 줄어든 그래프 라플라시안 행렬에서 구한 다음, 원래의 고유값과 고유벡터를 근사화시키는 Nystr${\ddot{o}}$m 기법을 주로 채택한다. 이 과정에서 많은 오차가 발생하는데, 이를 개선하기 위하여 본 논문에서는 그래프 라플라시안 대신에 가중치 행렬을 표본화하고 이로부터 구한 고유값과 고유벡터를 그래프 라플라시안의 고유값과 고유벡터로 변환하는 기법을 이용하여 대용량 데이터로 구성된 스펙트럴 그래프를 근사적으로 컴뮤트 타임 임베딩하는 기법을 제안한다. 하지만, 이 방식도 스펙트럼 분해를 계산하여야 하므로 데이터의 크기가 증가하면 적용하기 어려운 문제가 발생한다. 이의 대안으로, 스펙트럼 분해를 계산하지 않고도 데이터 집합의 크기에 영향을 받지 않으면서 컴뮤트 타임을 근사적으로 계산하는 방식을 구현하고 이들의 특성을 실험적으로 분석한다.

• Steel and Composite Structures
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• 제29권6호
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• pp.703-716
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• 2018

Rapid detection of damages in civil engineering structures, in order to assess their possible disorders and as a result produce competent decision making, are crucial to ensure their health and ultimately enhance the level of public safety. In traditional intelligent health monitoring methods, the features are manually extracted depending on prior knowledge and diagnostic expertise. Inspired by the idea of unsupervised feature learning that uses artificial intelligence techniques to learn features from raw data, a two-stage learning method is proposed here for intelligent health monitoring of civil engineering structures. In the first stage, $Nystr{\ddot{o}}m$ method is used for automatic feature extraction from structural vibration signals. In the second stage, Moving Kernel Principal Component Analysis (MKPCA) is employed to classify the health conditions based on the extracted features. In this paper, KPCA has been implemented in a new form as Moving KPCA for effectively segmenting large data and for determining the changes, as data are continuously collected. Numerical results revealed that the proposed health monitoring system has a satisfactory performance for detecting the damage scenarios of a three-story frame aluminum structure. Furthermore, the enhanced version of KPCA methods exhibited a significant improvement in sensitivity, accuracy, and effectiveness over conventional methods.

• 로봇학회논문지
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• 제3권2호
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• pp.117-122
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• 2008

This paper presents a multi-robot localization based on multidimensional scaling (MDS) in spite of the existence of incomplete and noisy data. While the traditional algorithms for MDS work on the full-rank distance matrix, there might be many missing data in the real world due to occlusions. Moreover, it has no considerations to dealing with the uncertainty due to noisy observations. We propose a robust MDS to handle both the incomplete and noisy data, which is applied to solve the multi-robot localization problem. To deal with the incomplete data, we use the Nystr$\ddot{o}$m approximation which approximates the full distance matrix. To deal with the uncertainty, we formulate a Bayesian framework for MDS which finds the posterior of coordinates of objects by means of statistical inference. We not only verify the performance of MDS-based multi-robot localization by computer simulations, but also implement a real world localization of multi-robot team. Using extensive empirical results, we show that the accuracy of the proposed method is almost similar to that of Monte Carlo Localization(MCL).

• 한국지능정보시스템학회:학술대회논문집
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• 한국지능정보시스템학회 2007년도 추계학술대회
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• pp.357-361
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• 2007

This paper presents a multi-robot localization based on Bayesian Multidimensional Scaling (BMDS). We propose a robust MDS to handle both the incomplete and noisy data, which is applied to solve the multi-robot localization problem. To deal with the incomplete data, we use the Nystr${\ddot{o}}$m approximation which approximates the full distance matrix. To deal with the uncertainty, we formulate a Bayesian framework for MDS which finds the posterior of coordinates of objects by means of statistical inference. We not only verify the performance of MDS-based multi-robot localization by computer simulations, but also implement a real world localization of multi-robot team. Using extensive empirical results, we show that the accuracy of the proposed method is almost similar to that of Monte Carlo Localization(MCL).