• KSCE Journal of Civil and Environmental Engineering Research
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• v.26 no.2B
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• pp.131-137
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• 2006

We have investigated the properties of the Singular Spectrum Analysis (SSA) coupled with the Linear Recurrent Formula which made it possible to complement the parametric time series model. The SSA has been applied to extract the underlying properties of the principal component of hydrologic time series, which can often be identified as trends, seasonalities and other oscillatory series, or noise components. Generally, the prediction by the SSA method can be applied to hydrologic time series governed (may be approximately) by the linear recurrent formulae. This study has examined the forecasting ability of the SSA-LRF model. These methods were applied to monthly discharge and water surface level data. These models indicated that two of the time series have good abilities of forecasting, particularly showing promising results during the period of one year. Thus, the method presented in this study suggests a competitive methodology for the forecast of hydrologic time series.

• Journal of the Korean Mathematical Society
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• v.38 no.3
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• pp.561-575
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• 2001

Making use of the singular spectrum in the Denjoy-Carleman class we prove the microlocal decomposition theorem and quasianalytic versions of Holmgren's uniqueness theorem and watermelon theorem.

• Proceedings of the Korea Water Resources Association Conference
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• 2006.05a
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• pp.1474-1478
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• 2006

본 연구에서는 여러 기상지수들과 우리나라 기온, 강수량에 대해서 Multi-Channel Singular Spectrum Analysis(MSSA)를 실시함으로써 상호영향에 따른 주성분을 분석하였다. Window length가 150일 때 SOI 등의 기상지수와 기온, 강수량의 MSSA를 실시하였으며 이 때 각각의 eigenvalue는 전체 공분산에 대한 각 요소의 비율을 설명한다. Window length는 Vautard 등(1992)이 제시한 $N/5{\sim}N/3$의 값을 사용하였다. 기상요소들과 기온, 강수량의 MSSA를 이용한 기후변화에 따른 국내 수문변수의 변화 상관분석은 기온과 각 기상요소들과의 분석결과에 비해 강수와 각 기상요소들의 분석결과가 기상요소들에 대한 주기패턴을 잘 따르지 못하고 약한 진폭을 나타내며 특히 SOI와 Rainfall의 경우 첫 번째 주성분에서의 상관분석결과 3개월 지체 시 상관계수 0.8410의 상관성이 높은 장주기 변화 쌍을 가짐에도 불구하고 자료의 변화도에 대하여 각 요소가 설명하는 비중이 매우 낮았다.

• ETRI Journal
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• v.37 no.4
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• pp.824-832
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• 2015

Heart sounds are the main obstacle in lung sound analysis. To tackle this obstacle, we propose a diagnosis algorithm that uses singular spectrum analysis (SSA) and frequency features of heart and lung sounds. In particular, we introduce a frequency coefficient that shows the frequency difference between heart and lung sounds. The proposed algorithm is applied to a synthetic mixture of heart and lung sounds. The results show that heart sounds can be extracted successfully and localizations for the first and second heart sounds are remarkably performed. An error analysis of the localization results shows that the proposed algorithm has fewer errors compared to the SSA method, which is one of the most powerful methods in the localization of heart sounds. The presented algorithm is also applied in the cases of recorded respiratory sounds from the chest walls of five healthy subjects. The efficiency of the algorithm in extracting heart sounds from the recorded breathing sounds is verified with power spectral density evaluations and listening. Most studies have used only normal respiratory sounds, whereas we additionally use abnormal breathing sounds to validate the strength of our achievements.

• Proceedings of the Korea Water Resources Association Conference
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• 2006.05a
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• pp.1479-1482
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• 2006

본 연구는 우리나라 강수자료 중 90년 이상의 자료를 보유한 지점(서울, 인천, 목포, 부산)에 대해서 변화도 분석과 Singular Spectrum Analysis(SSA)를 사용하여 자료의 주성분 및 주기성을 분석하였다. 각 자료의 변화도 분석결과 1907에서 2004년까지 98년간의 장기변화 중 선형추세에 의한 강우변화량은 23-11mm/mon 증가한다. 선형추세에 의한 년 강우변화량은 276-132mm/yr 이며 증분의 약 65%가 8월 증가량으로 과거 30년 강우분포는 7월에만 피크를 가지나 최근 30년의 강우분포는 7월과 8월에 비슷한 피크를 가지는 변화를 보일 뿐 아니라 지역에 따라 상이한 분포 양상을 보였다. 강우의 선형적 증가와 함께 변화폭도 증가하며 서울, 인천지역이 목포, 부산지역보다 큰 증가 양상을 보였다. 월 변화패턴과 선형추세 등 확정적 변화를 제거한 anomaly는 장기 변동과 각 달에 대해 다른 변동 폭을 가지는 noise의 합의 형태로 나타난다. Moving ave rage를 이용한 장기변동양상은 특정 주기를 가지지 않을 뿐만 아니라 변동 폭도 noise의 변동 폭에 비하여 미소하다. SSA결과 첫 번째 주성분이 전체변화의 1.7%이며 30번째 성분은 전체변화의 약 1% 정도로 장주기의 변화를 보였으나 전체자료에 비해 각 요소들이 설명하는 비중이 상당히 낮았다.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.26 no.6
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• pp.1461-1470
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• 2016

In side channel analysis, signal processing techniques can be used as preprocessing to enhance the efficiency and performance of analysis by reducing the noise or compressing the dimension. As signal processing techiniques using singular value decomposition can increase the information of main signal and reduce the noise by using the variance and tendency of signal, it is a great help to improve the performance of analysis. Typical techniques of that are PCA(Principal Component Analysis), LDA(Linear Discriminant Analysis) and SSA(Singular Spectrum Analysis). PCA and LDA can compress the dimension with increasing the information of main signal, and SSA reduces the noise by decomposing the signal into main siganl and noise. When applying each one or combination of these techniques, it is necessary to compare the performance. Therefore, it needs to suggest methodology of that. In this paper, we compare the performance of the three technique and propose using Sinal-to-Noise Ratio(SNR) as the methodology. Through the proposed methodology and various experiments, we confirm the performance and efficiency of each technique. This will provide useful information to many researchers in the field of side channel analysis.

• Journal of applied mathematics & informatics
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• v.38 no.1_2
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• pp.175-187
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• 2020

Recently Salkuyeh and Rahimian in (Comput. Math. Appl. 74 (2017) 2940-2949) proposed a modification of the generalized shift-splitting (MGSS) method for solving singular saddle point problems. In this paper, we present the spectral analysis of the MGSS preconditioner when it is applied to precondition the singular saddle point problems with the (1, 1) block being symmetric. Some eigenvalue bounds for the spectrum of the preconditioned matrix are given. We show that all the real eigenvalues of the preconditioned matrix are in a positive interval and all nonzero eigenvalues having nonzero imaginary part are contained in an intersection of two circles.

• Journal of Korean Society of Water and Wastewater
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• v.18 no.6
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• pp.758-769
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• 2004

The trends and seasonalities of most time series have a large variability. The result of the Singular Spectrum Analysis(SSA) processing is a decomposition of the time series into several components, which can often be identified as trends, seasonalities and other oscillatory series, or noise components. Generally, forecasting by the SSA method should be applied to time series governed (may be approximately) by linear recurrent formulae(LRF). This study examined forecasting ability of SSA-LRF model. These methods are applied to daily water demand data. These models indicate that most cases have good ability of forecasting to some extent by considering statistical and visual assessment, in particular forecasting validity shows good results during 15 days.

• Kyungpook Mathematical Journal
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• v.50 no.1
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• pp.15-35
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• 2010

By strengthening dichotomy condition and weakening decay conditions, we show that a four term 2n-th order differential operator with unbounded coefficients is nonlimit-point. Using stringent conditions we show that the deficiency index of this operator is determined by the behaviour of the coefficients themselves. Similarly, we prove the absence of singular continuous spectrum and that the absolutely continuous spectrum has multiplicity two.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.31 no.2B
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• pp.121-128
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• 2011

The paper presents trend analyses of the past 60-year-data of intensity (central pressure) and duration of the typhoons that influenced the Korean Peninsula. The singular spectrum analysis was employed to extract the trends. The result of linear regression of the trend component shows that the intensity of typhoons is slightly increased. A long-term change with period of about 30 years was detected, and thus the original series were separated into two sub-periods of 30 years. For these sub-periods, normal and Gumbel distributions of central pressure and duration of typhoons were estimated. The results show that during the second sub-period the overall intensity of typhoon was increased but the occurrence of extreme typhoons remains unchanged. The duration also showed an obvious increase during the second sub-period.