• The Journal of Korea Institute of Information, Electronics, and Communication Technology
• /
• v.12 no.5
• /
• pp.521-528
• /
• 2019

Epilepsy is one of the most prevalent neurological diseases. Electroencephalogram (EEG) signals are widely used for monitoring and diagnosis tool for epileptic seizure. Typically, a huge amount of EEG signals is needed, where they are visually examined by experienced clinicians. In this study, we propose a simple automatic seizure detection framework using intracranial EEG signals. We suggest a sparse approximation based classification (SAC) scheme by solving overdetermined system. L1-norm minimization algorithms are utilized for efficient sparse signal recovery. For evaluation of the proposed scheme, the public EEG dataset obtained by five healthy subjects and five epileptic patients is utilized. The results show that the proposed fast L1-norm minimization based SAC methods achieve the 99.5% classification accuracy which is 1% improved result than the conventional L2 norm based method with negligibly increased execution time (42msec).

• Proceedings of the Korean Society of Broadcast Engineers Conference
• /
• 2010.07a
• /
• pp.50-52
• /
• 2010

통신 시스템의 성능을 향상시키는 핵심 문제 중에 하나인 채널을 추정하는 문제는 다양한 분야에서 연구되고 있다. 채널의 sparse한 특징으로 인해 기존의 linear square나 minimum mean square error보다 발전된 $l_1$-norm minimization 방법 등이 많이 연구되고 있다. 이에 본 논문은 sparse한 채널의 특징과 천천히 변화하는 채널환경 특징을 이용하여 기존의 방법에 비해 더 높은 성능의 채널 추정 기법을 연구한다. 천천히 변화하는 채널환경의 특징으로 인해 이전 채널 정보를 현재 채널 추정에 사용할 수 있고 sparse한 채널의 특징으로 $l_1$-norm minimization을 사용할 수 있다. 이러한 두 가지의 정보를 이용하여 weighted $l_1$-norm minimization 이용한 support detection후 MMSE를 이용한 채널 추정기법을 연구한다.

• Journal of the Korean Institute of Telematics and Electronics
• /
• v.22 no.2
• /
• pp.82-89
• /
• 1985

A new non-inferior solution is obtained by investigating method of weight p- norm to explain the conception of MCO (multiple criterion optimization) problem. And then the optimum non-inferior solution is obtained by the weight minimization method applied to objective function of MOSFET NAND rATEAlso this weight minimization method using weight P- norm methods can be applied to non-convex objective function. The result of this minimization method shows the efficiency in comparison with that of Lightner.

• The Journal of the Acoustical Society of Korea
• /
• v.38 no.5
• /
• pp.543-548
• /
• 2019

The tonal signal caused by the machinery component of a vessel such as an engine, gearbox, and support elements, can be modeled as a sparse signal in the frequency domain. Recently, compressive sensing based techniques that recover an original signal using a small number of measurements in a short period of time, have been applied for the tonal frequency detection. These techniques, however, cannot avoid a basis mismatch error caused by the discretization of the frequency domain. In this paper, we propose a method to detect the tonal frequency with a small number of measurements in the continuous domain by using the atomic norm minimization technique. From the simulation results, we demonstrate that the proposed technique outperforms conventional methods in terms of the exact recovery ratio and mean square error.

• Journal of Advanced Marine Engineering and Technology
• /
• v.37 no.7
• /
• pp.743-751
• /
• 2013

In this paper, an approach to deal with model uncertainty using norm-optimal iterative learning control (ILC) is mentioned. Model uncertainty generally degrades the convergence and performance of conventional learning algorithms. To deal with model uncertainty, a worst-case norm-optimal ILC is introduced. The problem is then reformulated as a convex minimization problem, which can be solved efficiently to generate the control signal. The paper also investigates the relationship between the proposed approach and conventional norm-optimal ILC; where it is found that the suggested design method is equivalent to conventional norm-optimal ILC with trial-varying parameters. Finally, simulation results of the presented technique are given.

• Geophysics and Geophysical Exploration
• /
• v.10 no.2
• /
• pp.124-130
• /
• 2007

Least squares ($l^2$ norm) solutions of seismic inversion tend to be very sensitive to data points with large errors. The $l^1$ norm minimization gives more robust solutions, but usually with higher computational cost. Iteratively reweighted least squares (IRLS) method gives efficient approximate solutions of these $l^1$ norm problems. I propose an efficient implementation of the IRLS method for a hybrid $l^1/l^2$ minimization problem that behaves as $l^2$ norm fit for small residual and $l^1$ norm fit for large residuals. The proposed algorithm shows more robust characteristics to the decision of the threshold value than the l1 norm IRLS inversion does with respect to the threshold value to avoid singularity.

• Journal of the Institute of Convergence Signal Processing
• /
• v.19 no.4
• /
• pp.147-152
• /
• 2018

Underwater transient signals are complex, variable and nonlinear, resulting in a difficulty in accurate modeling with reference patterns. We analyze one type of underwater transient signals, in the form of whale sounds, using the MFCC(Mel-Frequency Cepstral Constant) and synthesize them from the MFCC and the weighted $L_2$-norm minimization techniques. The whales in this experiments are Humpback whales, Right whales, Blue whales, Gray whales, Minke whales. The 20th MFCC coefficients are extracted from the original signals using the MATLAB programming and reconstructed using the weighted $L_2$-norm minimization with the inverse MFCC. Finally, we could find the optimum weighted factor, 3~4 for reconstruction of whale sounds.

• 한국지구물리탐사학회:학술대회논문집
• /
• 2005.05a
• /
• pp.227-232
• /
• 2005

Least squares (${\ell}^2-norm$) solutions of seismic inversion tend to be very sensitive to data points with large errors. The ${\ell}^p-norm$ minimization for $1{\le}p<2$ gives more robust solutions, but usually with higher computational cost. Iteratively reweighted least squares (IRLS) gives efficient approximate solutions of these ${\ell}^p-norm$ problems. I propose a simple way to implement the IRLS method for a hybrid ${\ell}^1/{\ell}^2$ minimization problem that behaves as ${\ell}^2$ fit for small residual and ${\ell}^1$ fit for large residuals. Synthetic and a field-data examples demonstrates the improvement of the hybrid method over least squares when there are outliers in the data.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.12 no.7
• /
• pp.3194-3216
• /
• 2018

Slow Feature Discriminant Analysis (SFDA) is a supervised feature extraction method inspired by biological mechanism. In this paper, a novel method called Two Dimensional Slow Feature Discriminant Analysis via $L_{2,1}$ norm minimization ($2DSFDA-L_{2,1}$) is proposed. $2DSFDA-L_{2,1}$ integrates $L_{2,1}$ norm regularization and 2D statically uncorrelated constraint to extract discriminant feature. First, $L_{2,1}$ norm regularization can promote the projection matrix row-sparsity, which makes the feature selection and subspace learning simultaneously. Second, uncorrelated features of minimum redundancy are effective for classification. We define 2D statistically uncorrelated model that each row (or column) are independent. Third, we provide a feasible solution by transforming the proposed $L_{2,1}$ nonlinear model into a linear regression type. Additionally, $2DSFDA-L_{2,1}$ is extended to a bilateral projection version called $BSFDA-L_{2,1}$. The advantage of $BSFDA-L_{2,1}$ is that an image can be represented with much less coefficients. Experimental results on three face databases demonstrate that the proposed $2DSFDA-L_{2,1}/BSFDA-L_{2,1}$ can obtain competitive performance.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.25 no.3
• /
• pp.107-116
• /
• 2021

We introduce optimization algorithms using Bregman Divergence for solving non-negative matrix factorization (NMF) problems. Bregman divergence is known a generalization of some divergences such as Frobenius norm and KL divergence and etc. Some algorithms can be applicable to not only NMF with Frobenius norm but also NMF with more general Bregman divergence. Matrix Factorization is a popular non-convex optimization problem, for which alternating minimization schemes are mostly used. We develop the Bregman proximal gradient method applicable for all NMF formulated in any Bregman divergences. In the derivation of NMF algorithm for Bregman divergence, we need to use majorization/minimization(MM) for a proper auxiliary function. We present algorithmic aspects of NMF for Bregman divergence by using MM of auxiliary function.