• Bulletin of the Korean Mathematical Society
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• v.55 no.4
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• pp.1303-1315
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• 2018

For principal component analysis (PCA) to efficiently analyze large scale matrices, it is crucial to find a few singular vectors in cheaper computational cost and under lower memory requirement. To compute those in a fast and robust way, we propose a new stochastic method. Especially, we adopt the stochastic variance reduced gradient (SVRG) method [11] to avoid asymptotically slow convergence in stochastic gradient descent methods. For that purpose, we reformulate the PCA problem as a unconstrained optimization problem using a quadratic penalty. In general, increasing the penalty parameter to infinity is needed for the equivalence of the two problems. However, in this case, exact penalization is guaranteed by applying the analysis in [24]. We establish the convergence rate of the proposed method to a stationary point and numerical experiments illustrate the validity and efficiency of the proposed method.

• Journal of Korea Multimedia Society
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• v.19 no.12
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• pp.1951-1959
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• 2016

In this paper, we propose a two-scale fusion method for infrared and visible images using saliency and variance. The images are separated into two scales respectively: a base layer of low frequency component and a detailed layer of high frequency component. Then, these are synthesized using weight. The saliencies and the variances of the images are used as the fusion weights for the two-scale images. The proposed method is tested on several image pairs, and its performance is evaluated quantitatively by using objective fusion metrics.

• Communications for Statistical Applications and Methods
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• v.2 no.2
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• pp.129-134
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• 1995

The ordinary least square estimator of the disturbance variance in the pooled cross-sectional and time series regression model is shown to be asymptotically unbiased without any restrictions on the regressor matrix when the disturbances follow an equicorrelated error component models.

• Journal of the Korea Society of Computer and Information
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• v.23 no.12
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• pp.21-26
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• 2018

As the large amount of data can be efficiently stored, the methods extracting meaningful features from big data has become important. Especially, the techniques of converting high- to low-dimensional data are crucial for the 'Data visualization'. In this study, principal component analysis (PCA; linear dimensionality reduction technique) and Isomap (non-linear dimensionality reduction technique) are introduced and applied to neural big data obtained by the functional magnetic resonance imaging (fMRI). First, we investigate how much the physical properties of stimuli are maintained after the dimensionality reduction processes. We moreover compared the amount of residual variance to quantitatively compare the amount of information that was not explained. As result, the dimensionality reduction using Isomap contains more information than the principal component analysis. Our results demonstrate that it is necessary to consider not only linear but also nonlinear characteristics in the big data analysis.

• Journal of the Korean Data and Information Science Society
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• v.7 no.1
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• pp.87-92
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• 1996

A regression model with nested erroe structure is considered. The regression model includes two error terms that are independent and normally distributed with zero means and constant variances. This error structure of the model gives correlated response variables. The distributions of variance components in the regression model with nested error structure are dervied by using theorems for quadratic forms.

• ETRI Journal
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• v.45 no.1
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• pp.131-137
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• 2023

The phase reconstruction process in digital holographic microscopy involves a trade-off between the phase error and the high-spatial-frequency components. In this reconstruction process, if the narrow region of the sideband is windowed in the Fourier domain, the phase error from the DC component will be reduced, but the high-spatial-frequency components will be lost. However, if the wide region is windowed, the 3D profile will include the high-spatial-frequency components, but the phase error will increase. To solve this trade-off, we propose the high-variance pixel averaging method, which uses the variance map of the reconstructed depth profiles of the windowed sidebands of different sizes in the Fourier domain to classify the phase error and the high-spatial-frequency components. Our proposed method calculates the average of the high-variance pixels because they include the noise from the DC component. In addition, for the nonaveraged pixels, the reconstructed phase data created by the spatial frequency components of the widest window are used to include the high-spatialfrequency components. We explain the mathematical algorithm of our proposed method and compare it with conventional methods to verify its advantages.

• East Asian mathematical journal
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• v.9 no.2
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• pp.333-345
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• 1993

• Journal of the Korean Data and Information Science Society
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• v.28 no.5
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• pp.981-999
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• 2017

In the standard control chart assuming a simple random model, we estimate the process variance without considering the between-sample variance. If the between-sample exists in the process, the process variance is under-estimated. When the process variance is under-estimated, the narrower control limits result in the excessive false alarm rate although the sensitivity of the control chart is improved. In this paper, using the variance component model to incorporate the between-sample variance, we set the control limits using both the within- and between-sample variances, and evaluate the efficiency of the control chart in terms of the average run length (ARL). Considering the most widely used control chart types such as ${\bar{X}}$, EWMA and CUSUM control charts, we compared the differences between two cases, Case I and Case II, where the between-sample variance is ignored and considered, respectively. We also considered the two cases when the process parameters are given and estimated. The results showed that the false alarm rate of Case I increased sharply as the between-sample variance increases, while that of Case II remains the same regardless of the size of the between-sample variance, as expected.

• Korean Journal of Food Science and Technology
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• v.44 no.5
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• pp.648-652
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• 2012

The sensory characteristics of nine commercially distilled soju samples were determined by sensory descriptive analysis. Eight aroma attributes, as well as four flavor/taste attributes, and six mouth-feel related attributes were evaluated by 9 judges. The descriptive data set was initially analyzed for a significant overall product effect by employing a three-way mixed model analysis of variance (judges, samples, and replications) as well as two-way interactions, with judges treated as random. In addition, correlations between mean attribute ratings were calculated, and a principal component analysis (PCA) of the mean attribute ratings employing the covariance matrix was conducted. Based on the PCA, distilled soju samples were primarily separated along the first principal component, which accounted for 66% of the total variance between the samples, with high intensities of 'alcohol taste' and 'alcohol aroma' versus 'yeast aroma'. The second principal component accounted for 14% of the total variance. Soju containing high alcohol showed stronger intensities of 'bitterness', 'alcohol taste', 'alcohol aroma', as well as all mouth-feel attributes.

• Science of Emotion and Sensibility
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• v.11 no.4
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• pp.553-564
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• 2008

Generalizability theory was employed to examine how the reliability of polygraph test is affected by the number of relevant questions, the number of repeated tests (the number of of charts), and the number of raters(scorers). The data consisted of the results of the polygraph tests administered to 31 crime suspects. The sample was drawn from the real polygraph tests based on Backster ZCT and archived by the Prosecutor's Office of the Republic of Korea. The numerical scores assigned by thirteen raters to the test charts were analyzed to determine the generalizability of the scores. The largest variance component was accounted for by the examinee factor(43.97%) and the residual variance component was 16.84% of the total variance. The variance component due to the interaction between the examinee and the chart factors was 12.17% and the variance component due to the three way interaction of the examinee, the repeated test, and the relevant question factors was 10.31%. The generalizability coefficient for the current measurement procedure as practiced by the Korean Prosecutor's Office was 0.74 which suggests that the current procedure is acceptable. However, measurement procedures with the combination of more than two relevant questions, more than three repeated tests, and more than two raters were generally found to yield generalizability coefficients larger than 0.80. Therefore, such procedures need to be considered seriously in order to significantly improve the reliability of polygraph test.