• Journal of the Korean Mathematical Society
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• v.56 no.6
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• pp.1503-1514
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• 2019

A rank 1 matrix has a factorization as $uv^t$ for vectors u and v of some orders. The arctic rank of a rank 1 matrix is the half number of nonzero entries in u and v. A matrix of rank k can be expressed as the sum of k rank 1 matrices, a rank 1 decomposition. The arctic rank of a matrix A of rank k is the minimum of the sums of arctic ranks of the rank 1 matrices over all rank 1 decomposition of A. In this paper we obtain characterizations of the linear operators that strongly preserve the symmetric arctic ranks of symmetric matrices over nonnegative reals.

• Journal of the Korean Institute of Intelligent Systems
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• v.15 no.5
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• pp.599-604
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• 2005

This paper presents fuzzy rules to predict diagnosis of Wisconsin breast cancer with minimized number of feature in put using the neural network with weighted fuzzy membership functions (NEWFM) and the non-overlap area distribution measurement method. NEWFM is capable of self-adapting weighted membership functions from the given the Wisconsin breast cancer clinical training data. n set of small, medium, and large weighted triangular membership functions in a hyperbox are used for representing n set of featured input. The membership functions are randomly distributed and weighted initially, and then their positions and weights are adjusted during learning. After learning, prediction rules are extracted directly from n set of enhanced bounded sums of n set of small, medium, and large weighted fuzzy membership functions. Then, the non-overlap area distribution measurement method is applied to select important features by deleting less important features. Two sets of prediction rules extracted from NEWFM using the selected 4 input features out of 9 features outperform to the current published results in number of set of rules, number of input features, and accuracy with 99.71%.

• The Journal of the Acoustical Society of Korea
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• v.16 no.4
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• pp.57-63
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• 1997

In this paper, we study the efficient feature vector extraction method and front-end processing to improve the performance of the speech recognition system using KT(Korea Telecommunication) database collected through various telephone channels. First of all, we compare the recognition performances of the feature vectors known to be robust to noise and environmental variation and verify the performance enhancement of the recognition system using weighted cepstral distance measure methods. The experiment result shows that the recognition rate is increasedby using both PLP(Perceptual Linear Prediction) and MFCC(Mel Frequency Cepstral Coefficient) in comparison with LPC cepstrum used in KT recognition system. In cepstral distance measure, the weighted cepstral distance measure functions such as RPS(Root Power Sums) and BPL(Band-Pass Lifter) help the recognition enhancement. The application of the spectral subtraction method decrease the recognition rate because of the effect of distortion. However, RASTA(RelAtive SpecTrAl) processing, CMS(Cepstral Mean Subtraction) and SBR(Signal Bias Removal) enhance the recognition performance. Especially, the CMS method is simple but shows high recognition enhancement. Finally, the performances of the modified methods for the real-time implementation of CMS are compared and the improved method is suggested to prevent the performance degradation.

• The Korean Journal of Applied Statistics
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• v.27 no.1
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• pp.61-70
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• 2014

A randomized block design is a method to apply a treatment into the experimental unit of each block after dividing into several blocks with a binded homogeneous experimental unit. Jonckheere (1964) and Terpstra (1952), Page (1963), Hollander (1967) proposed various methods of ordered alternative in randomized block design. Especially, Page (1963) test is a weighted combination of within block rank sums for ordered alternatives. In this paper, we suggest a new nonparametric method expanding the Page test for an ordered alternative. A Monte Carlo simulation study is also adapted to compare the power of the proposed methods with previous methods.

• IE interfaces
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• v.16 no.4
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• pp.485-495
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• 2003

This paper reports on the application of the integration of mathematical programming model and database in a decision support system (DSS) for the planning of the multi-reservoir operating system. The DSS is based on a multi-objective, mixed-integer goal programming (MIGP) model, which can generate efficient solutions via the weighted-sums method (WSM). The major concern of this study is seamless, efficient integration between the mathematical model and the database, because there are significant differences in structure and content between the data for a mathematical model and the data for a conventional database application. In order to load the external optimization results on the database, we developed a systematic way of naming variable/constraint so that a rapid identification of variables/constraints is possible. An efficient database structure for planning of the multi-reservoir operating system is presented by taking advantage of the naming convention of the variable/constraint.

• Bulletin of the Korean Mathematical Society
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• v.47 no.3
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• pp.467-482
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• 2010

For a double array of random elements {$V_{mn};m{\geq}1,\;n{\geq}1$} in a real separable Banach space, some mean convergence theorems and weak laws of large numbers are established. For the mean convergence results, conditions are provided under which $k_{mn}^{-\frac{1}{r}}\sum{{u_m}\atop{i=1}}\sum{{u_n}\atop{i=1}}(V_{ij}-E(V_{ij}|F_{ij})){\rightarrow}0$ in $L_r$ (0 < r < 2). The weak law results provide conditions for $k_{mn}^{-\frac{1}{r}}\sum{{T_m}\atop{i=1}}\sum{{\tau}_n\atop{j=1}}(V_{ij}-E(V_{ij}|F_{ij})){\rightarrow}0$ in probability where {$T_m;m\;{\geq}1$} and {${\tau}_n;n\;{\geq}1$} are sequences of positive integer-valued random variables, {$k_{mn};m{{\geq}}1,\;n{\geq}1$} is an array of positive integers. The sharpness of the results is illustrated by examples.

• Journal of information and communication convergence engineering
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• v.21 no.3
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• pp.208-215
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• 2023

Deep learning techniques provide powerful solutions to several pattern-recognition problems, including Raman spectral classification. However, these networks require large amounts of labeled data to perform well. Labeled data, which are typically obtained in a laboratory, can potentially be alleviated by data augmentation. This study investigated various data augmentation techniques and applied multiple deep learning methods to Raman spectral classification. Raman spectra yield fingerprint-like information about chemical compositions, but are prone to noise when the particles of the material are small. Five augmentation models were investigated to build robust deep learning classifiers: weighted sums of spectral signals, imitated chemical backgrounds, extended multiplicative signal augmentation, and generated Gaussian and Poisson-distributed noise. We compared the performance of nine state-of-the-art convolutional neural networks with all the augmentation techniques. The LeNet5 models with background noise augmentation yielded the highest accuracy when tested on real-world Raman spectral classification at 88.33% accuracy. A class activation map of the model was generated to provide a qualitative observation of the results.

• The Journal of Society for e-Business Studies
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• v.22 no.1
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• pp.15-35
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• 2017

The method of weighted sum of evaluation using AHP is widely used in feasibility analysis and alternative selection. Final scores are given in forms of weighted sums and the alternative with largest score is selected. With two alternatives, as in feasibility analysis, the final score greater than 0.5 gives the selection but there remains a question that how large is large enough. KDI suggested a concept of 'grey area' where scores are between 0.45 and 0.55 in which decisions are to be made with caution, but it lacks theoretical background. Statistical testing was introduced to answer the question in some studies. It was assumed some kinds of probability distribution, but did not give the validity on them. We examine the various cases of weighted sum of evaluation score and show why the statistical testing has to be introduced. We suggest a non-parametric testing procedure which does not assume a specific distribution. A case study is conducted to analyze the validity of our suggested testing procedure. We conclude our study with remarks on the implication of analysis and the future way of research development.

• The Korean Journal of Applied Statistics
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• v.5 no.2
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• pp.243-254
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• 1992

In the present study two sets of unbalanced two-way cross-classification data with and without empty cell(s) were used to evaluate empirically the various sums of squares in the analysis of variance table. Searle(1977) and Searle et.al.(1981) developed a method of computing R($\alpha$\mid$\mu, \beta$) and R($\beta$\mid$\mu, \alpha$) by the use of partitioned matrix of X'X for the model of no interaction, interchanging the columns of X in order of $\alpha, \mu, \beta$ and accordingly the elements in b. An alternative way of computing R($\alpha$\mid$\mu, \beta$), R($\beta$\mid$\mu, \alpha$) and R($\gamma$\mid$\mu, \alpha, \beta$) without interchanging the columns of X has been found by means of,$(X'X)^-$ derived, using $W_2 = Z_2Z_2-Z_2Z_1(Z_1Z_1)^-Z_1Z_2$. It is true that $R(\alpha$\mid$\mu,\beta,\gamma)\Sigma = SSA_W and R(\beta$\mid$\mu,\alpha,\gamma)\Sigma = SSB_W$ where $SSA_W$ and means analysis and $R(\gamma$\mid$\mu,\alpha,\beta) = R(\gamma$\mid$\mu,\alpha,\beta)\Sigma$ for the data without empty cell, but not for the data with empty cell(s). It is also noticed that for the datd with empty cells under W - restrictions $R(\alpha$\mid$\mu,\beta,\gamma)_W = R(\mu,\alpha,\beta,\gamma)_W - R(\mu,\alpha,\beta,\gamma)_W = R(\alpha$\mid$\mu) and R(\beta$\mid$\mu,\alpha,\gamma)_W = R(\mu,\alpha,\beta,\gamma)_W - R(\mu,\alpha,\beta,\gamma)_W = R(\beta$\mid$\mu) but R(\gamma$\mid$\mu,\alpha,\beta)_W = R(\mu,\alpha,\beta,\gamma)_W - R(\mu,\alpha,\beta,\gamma)_W \neq R(\gamma$\mid$\mu,\alpha,\beta)$. The hypotheses $H_o : K' b = 0$ commonly tested were examined in the relation with the corresponding sums of squares for $R(\alpha$\mid$\mu), R(\beta$\mid$\mu), R(\alpha$\mid$\mu,\beta), R(\beta$\mid$\mu,\alpha), R(\alpha$\mid$\mu,\beta,\gamma), R(\beta$\mid$\mu,\alpha,\gamma), and R(\gamma$\mid$\mu,\alpha,\beta)$ under the restrictions.