• Journal of the Korean Mathematical Society
• /
• v.57 no.6
• /
• pp.1471-1484
• /
• 2020

It may very well be difficult to prove an eigenvalue inequality of Payne-Pólya-Weinberger type for the bi-drifting Laplacian on the bounded domain of the general complete metric measure spaces. Even though we suppose that the differential operator is bi-harmonic on the standard Euclidean sphere, this problem still remains open. However, under certain condition, a general inequality for the eigenvalues of bi-drifting Laplacian is established in this paper, which enables us to prove an eigenvalue inequality of Ashbaugh-Cheng-Ichikawa-Mametsuka type (which is also called an eigenvalue inequality of Payne-Pólya-Weinberger type) for the eigenvalues with lower order of bi-drifting Laplacian on the Gaussian shrinking soliton.

• 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.

• Proceedings of the IEEK Conference
• /
• 2003.07e
• /
• pp.2004-2007
• /
• 2003

This paper describes a method of performance enhancement using Flatness Mesure(FM) for the Gaussian Mixture Model(GMM) face recognition systems. Using this measure we discard the frames having low information before training and test. As the result, the performance increases about 9％ in the lower mixtures and calculation burden is decreased. As well, the recognition error rate is decreased under the illumination change surroundings. We use the 2D DCT coefficients lot face feature vectors and experiments are carried out on the Olivetti Research Laboratory (ORL) face database.

• Bulletin of the Korean Mathematical Society
• /
• v.42 no.2
• /
• pp.231-244
• /
• 2005

We derive a comparison theorem for solutions of the following stochastic partial differential equations in a Hilbert space H. $$Lu^i=\alpha(u^i)M(t,\; x)+\beta^i(u^i),\;for\;i=1,\;2,$$ $where\;Lu^i=\;\frac{\partial u^i}{\partial t}\;-\;Au^{i}$, A is a linear closed operator on Hand M(t, x) is a spatially homogeneous Gaussian noise with covariance of a certain form. We are going to show that if $\beta^1\leq\beta^2\;then\;u^1{\leq}u^2$ under some conditions.

• Journal of the Korea Institute of Information and Communication Engineering
• /
• v.11 no.11
• /
• pp.2158-2165
• /
• 2007

In this paper, a Modified Fuzzy C-Means algorithm with Gaussian Weights(MFCM_GW) is presented for nonlinear blind channel equalization. The proposed algorithm searches the optimal channel output states of a nonlinear channel from the received symbols, based on the Bayesian likelihood fitness function and Gaussian weighted partition matrix instead of a conventional Euclidean distance measure. Next, the desired channel states of a nonlinear channel are constructed with the elements of estimated channel output states, and placed at the center of a Radial Basis Function(RBF) equalizer to reconstruct transmitted symbols. In the simulations, binary signals are generated at random with Gaussian noise. The performance of the proposed method is compared with those of a simplex genetic algorithm(GA), a hybrid genetic algorithm(GA merged with simulated annealing(SA): GASA), and a previously developed version of MFCM. It is shown that a relatively high accuracy and fast search speed has been achieved.

• Journal of Korean Society for Atmospheric Environment
• /
• v.23 no.4
• /
• pp.449-456
• /
• 2007

Dispersion coefficient preprocessing schemes have been examined to improve plume dispersion model performance in complex coastal areas. The performances of various schemes for constructing the sigma correction order were evaluated through estimations of statistical measures, such as bias, gross error, R, FB, NMSE, within FAC2, MG, VG, IOA, UAPC and MRE. This was undertaken for the results of dispersion modeling, which applied each scheme. Environmental factors such as sampling time, surface roughness, plume rising, plume height and terrain rolling were considered in this study. Gaussian plume dispersion model was used to calculate 1 hr $SO_2$ concentration 4 km downwind from a power plant in Boryeung coastal area. Here, measured data for January to December of 2002 were obtained so that modelling results could be compared. To compare the performances between various schemes, integrated scores of statistical measures were obtained by giving weights for each measure and then summing each score. This was done because each statistical measure has its own function and criteria; as a result, no measure can be taken as a sole index indicative of the performance level for each modeling scheme. The best preprocessing scheme was discerned using the step-wise method. The most significant factor influencing the magnitude of real dispersion coefficients appeared to be sampling time. A second significant factor appeared to be surface roughness, with the rolling terrain being the least significant for elevated sources in a gently rolling terrain. The best sequence of correcting the sigma from P-G scheme was found to be the combination of (1) sampling time, (2) surface roughness, (3) plume rising, (4) plume height, and (5) terrain rolling.

• ETRI Journal
• /
• v.38 no.3
• /
• pp.540-550
• /
• 2016

Spectral clustering is a powerful tool for exploratory data analysis. Many existing spectral clustering algorithms typically measure the similarity by using a Gaussian kernel function or an undirected k-nearest neighbor (kNN) graph, which cannot reveal the real clusters when the data are not well separated. In this paper, to improve the spectral clustering, we consider a robust similarity measure based on the shared nearest neighbors in a directed kNN graph. We propose two novel algorithms for spectral clustering: one based on the number of shared nearest neighbors, and one based on their closeness. The proposed algorithms are able to explore the underlying similarity relationships between data points, and are robust to datasets that are not well separated. Moreover, the proposed algorithms have only one parameter, k. We evaluated the proposed algorithms using synthetic and real-world datasets. The experimental results demonstrate that the proposed algorithms not only achieve a good level of performance, they also outperform the traditional spectral clustering algorithms.

• Journal of Korea Technical Association of The Pulp and Paper Industry
• /
• v.35 no.3
• /
• pp.43-52
• /
• 2003

The new principle to measure a sizing degree by a contact angle was developed using an automatic determination of the 3-end point coordinates of the water droplet on a sheet, which could diminish the operator's bias during measurement. A constant amount of water was first placed on a sample sheet by a water dispenser, and then an image of the liquid droplet was captured by a digital camera and then transmitted to a computer. The program measuring for contact angle extracted a liquid contour by Gaussian function combined with a 8-direction chain code. The Euclidean equation was applied to the binary image of the liquid contour in order to measure the diameter of the contour. Finally, the contact angle of the liquid was calculated by using the diameter and the top coordinates. In addition, a surface free energy of the sample sheet and an elapsed time taken up to the complete absorption into the sheet were simultaneously measured with the contact angle.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.29 no.5C
• /
• pp.627-631
• /
• 2004

An efficient algorithm for clustering of GPDFs(Gaussian Probability Density Functions) in a speech recognition model is proposed in this paper. The proposed algorithm is based on CNN with the divergence as its distance measure and is applied to a speech recognition. The algorithm is compared with conventional Dk-means(Divergence-based k-means) algorithm in CDHMM(Continuous Density Hidden Markov Model). The results show that it can reduce about 31.3％ of GPDFs over Dk-means algorithm without suffering any recognition performance. When compared with the case that no clustering is employed and full GPDFs are used, the proposed algorithm can save about 61.8％ of GPDFs while preserving the recognition performance.

• The Journal of the Acoustical Society of Korea
• /
• v.30 no.7
• /
• pp.383-389
• /
• 2011

In this paper, we propose a improved speech absence probability estimation algorithm by applying environmental noise classification for speech enhancement. The previous speech absence probability required to seek a priori probability of speech absence was derived by applying microphone input signal and the noise signal based on the estimated value of a posteriori SNR threshold. In this paper, the proposed algorithm estimates the speech absence probability using noise classification algorithm which is based on Gaussian mixture model in order to apply the optimal parameter each noise types, unlike the conventional fixed threshold and smoothing parameter. Performance of the proposed enhancement algorithm is evaluated by ITU-T P.862 PESQ (perceptual evaluation of speech quality) and composite measure under various noise environments. It is verified that the proposed algorithm yields better results compared to the conventional speech absence probability estimation algorithm.