• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.25 no.4
• /
• pp.162-172
• /
• 2021

This paper proposes stochastic methods to find an approximate solution for the L²-Wasserstein least squares problem of Gaussian measures. The variable for the problem is in a set of positive definite matrices. The first proposed stochastic method is a type of classical stochastic gradient methods combined with projection and the second one is a type of variance reduced methods with projection. Their global convergence are analyzed by using the framework of proximal stochastic gradient methods. The convergence of the classical stochastic gradient method combined with projection is established by using diminishing learning rate rule in which the learning rate decreases as the epoch increases but that of the variance reduced method with projection can be established by using constant learning rate. The numerical results show that the present algorithms with a proper learning rate outperforms a gradient projection method.

• KIPS Transactions on Software and Data Engineering
• /
• v.3 no.6
• /
• pp.215-218
• /
• 2014

In hashing-based methods for approximate nearest neighbors(ANN) search, by mapping data points to k-bit binary codes, nearest neighbors are searched in a binary embedding space. In this paper, we present a hashing method using a PCA-based clustering method, Principal Direction Divisive Partitioning(PDDP). PDDP is a clustering method which repeatedly partitions the cluster with the largest variance into two clusters by using the first principal direction. The proposed hashing method utilizes the first principal direction as a projective direction for binary coding. Experimental results demonstrate that the proposed method is competitive compared with other hashing methods.

• The Journal of the Korea Contents Association
• /
• v.9 no.9
• /
• pp.68-79
• /
• 2009

A variance map can be used to detect and distinguish texts from background in images. However, previous variance maps work at one level and they suffer a limitation in dealing with varieties in text size, slant, orientation, translation, and color. We present a method for robustly segmenting text regions in complex color Web images using two-level variance maps. The two-level variance maps work hierarchically. The first level finds the approximate locations of text regions using global horizontal and vertical color variances with the specific mask sizes. The second level then segments each text region using intensity variance with a local mask size, which is determined adaptively. By the second process, backgrounds tend to disappear in each region and segmentation can be accurate. Highly promising experimental results have established the effectiveness of our approach.

• Journal of the Korea Safety Management & Science
• /
• v.12 no.1
• /
• pp.199-205
• /
• 2010

The research proposes the three-factor random measurement models for estimating the precision about operator, part, tool, and various measurement environments. The combined model with crossed and nested factors is developed to analyze the approximate F test by degrees of freedom given by Satterthwaite and point estimation of precisions from expected mean square. The model developed in this paper can be extended to the three useful models according to the type of nested designs. The study also provides the three-step procedures to evaluate the measurement precisions using three indexes such as SNR(Signal-To-Noise Ratio), R&R TR(Reproducibility&Repeatability-To-Total Precision Ratio), and PTR(Precision-To-Tolerance Ratio), The procedures include the identification of resolution, the improvement of R&R reduction, and the evaluation of precision effect.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.18 no.6
• /
• pp.1448-1454
• /
• 1994

Data which gathered and used in the field of fatigue and fracture mechanics have a lot of uncertainties. In this case, those uncertainties will make scatter band in evaluation of fatigue life and fracture toughness. Thus, the probabilistic analysis of these data will be needed. For determining the fatigue life in mixed mode, using crack direction law and fatigue crack growth law, the problem is studied as a constrained life minimization. Stress intensity factor(SIF) is computed by approximate solution table(Ewalds/Wanhill 1984) and 0th order PFEM. The variance of fatigue life and SIF are computed by differentiation of tabulated approximate solution and 1st order PFEM. And these are used for criterion of design values, principal parameter determination and modelling. The problem of center cracked plate is solved for checking the PFEM model which is influenced by various parameters like as initial crack length, final crack length, two fatigue parameters in Paris Equation and applied stress.

• Journal of Institute of Control, Robotics and Systems
• /
• v.12 no.12
• /
• pp.1256-1260
• /
• 2006

This paper presents an enhanced ${\alpha}-{\beta}$ tracking filter whose ${\alpha}-{\beta}$ gains are updated by an approximation method at every scan to account for the transition of measurement dependent observation error variance in two-dimensional Cartesian coordinates. The approximate ${\alpha}-{\beta}$ gains are calculated from the amount of the change in the tracking index and the partial derivatives of the ${\alpha}-{\beta}$ gains with respect to a nominal tracking index. It is shown via simulation that the proposed tracker provides improved performance compared to the conventional ${\alpha}-{\beta}$ tracking filter.

• Journal of Korean Society for Quality Management
• /
• v.21 no.1
• /
• pp.171-180
• /
• 1993

Variables, x and y are said to have a linear relation if $y={\beta}_0+{\beta}_1\;x$, and ${\beta}_0$ and ${\beta}_1$ are constants. The relationship is called a structural relationship if x has positive variance (i.e., x is not fixed) and only error-prone measurements of x and y can be obtained. This paper derives (to order $n^{+1/2}$) an approximate distribution of the Studentized test statistic for testing hypotheses about the slope parameter, ${\beta}_1$ in a simple linear structural model. A simulation study suggests our approximate distribution is more accurate approximation to the exact distributions of the Studentized statistic than is the limiting distribution.

• Journal of Mechanical Science and Technology
• /
• v.20 no.8
• /
• pp.1169-1182
• /
• 2006

Robust design technology has been applied to versatile engineering problems to ensure consistency in product performance. Since 1980s, the concept of robust design has been introduced to numerical optimization field, which is called the robust optimization. The robustness in the robust optimization is determined by a measure of insensitiveness with respect to the variation of a response. However, there are significant difficulties associated with the calculation of variations represented as its mean and variance. To overcome the current limitation, this research presents an implementation of the approximate statistical moment method based on kriging metamodel. Two sampling methods are simultaneously utilized to obtain the sequential surrogate model of a response. The statistics such as mean and variance are obtained based on the reliable kriging model and the second-order statistical approximation method. Then, the simulated annealing algorithm of global optimization methods is adopted to find the global robust optimum. The mathematical problem and the two-bar design problem are investigated to show the validity of the proposed method.

• Journal of Korean Society for Quality Management
• /
• v.27 no.1
• /
• pp.46-58
• /
• 1999

The exact distributions of the sample variance $(S^2_n)$ and the estimator ($\hat{C}_p$) of the process capability index are not easily obtained in general. In this paper, the approximations using saddlepoint techniques to the distributions of these statistics are suggested and compared with the other approximation methods. For comparisons, the exact values obtained by extensive Monte-Carlo (simulation) studies are also given. As a result, the suggested approximation methods are very accurate even in moderate or small sample sizes and are easy to use. Also, the suggested methods can be adapted to approximate the distributions of more complicated statistics, including $\hat{C}_pk$ ,$\hat{C}_pm$, etc.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.16 no.12
• /
• pp.4099-4113
• /
• 2022

In this paper, we propose improved maximum access delay time, noise variance, and power delay profile (PDP) estimation schemes for orthogonal frequency division multiplexing (OFDM) system in multipath fading channels. To this end, we adopt the approximate maximum likelihood (ML) estimation strategy. For the first step, the log-likelihood function (LLF) of the received OFDM symbols is derived by utilizing only the cyclic redundancy induced by cyclic prefix (CP) without additional information. Then, the set of the initial path powers is sub-optimally obtained to maximize the derived LLF. In the second step, we can select a subset of the initial path power set, i.e. the maximum access delay time, so as to maximize the modified LLF. Through numerical simulations, the benefit of the proposed method is verified by comparison with the existing methods in terms of normalized mean square error, erroneous detection, and good detection probabilities.