• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.2 no.2
• /
• pp.81-95
• /
• 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
• /
• v.21 no.3
• /
• pp.561-567
• /
• 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.

• Journal of the Institute of Electronics and Information Engineers
• /
• v.52 no.2
• /
• pp.162-170
• /
• 2015

Commute time embedding involves computing the spectral decomposition of the graph Laplacian. It requires the computational burden proportional to $o(n^3)$, not suitable for large scale dataset. Many methods have been proposed to accelerate the computational time, which usually employ the Nystr${\ddot{o}}$m methods to approximate the spectral decomposition of the reduced graph Laplacian. They suffer from the lost of information by dint of sampling process. This paper proposes to reduce the errors by approximating the spectral decomposition of the graph Laplacian using that of the affinity matrix. However, this can not be applied as the data size increases, because it also requires spectral decomposition. Another method called approximate commute time embedding is implemented, which does not require spectral decomposition. The performance of the proposed algorithms is analyzed by computing the commute time on the patch graph.

• Steel and Composite Structures
• /
• v.29 no.6
• /
• pp.703-716
• /
• 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.

• The Journal of Korea Robotics Society
• /
• v.3 no.2
• /
• pp.117-122
• /
• 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).

• Proceedings of the Korea Inteligent Information System Society Conference
• /
• 2007.11a
• /
• pp.357-361
• /
• 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).