• Journal of the Korean Data and Information Science Society
• /
• 제18권4호
• /
• pp.1135-1143
• /
• 2007

The singular value decomposition and the spectral decomposition are the useful methods in the area of matrix computation for multivariate techniques such as principal component analysis and multidimensional scaling. These techniques aim to find a simpler geometric structure for the data points. The singular value decomposition and the spectral decomposition are the methods being used in these techniques for this purpose. In this paper, the singular value decomposition and the spectral decomposition are compared.

• Communications for Statistical Applications and Methods
• /
• 제17권6호
• /
• pp.803-810
• /
• 2010

The singular value decomposition of a rectangular matrix is a basic tool to understand the structure of the data and particularly the relationship between row and column factors. However, conventional singular value decomposition used the least squares method and is not robust to outliers. We propose a simple robust singular value decomposition algorithm based on the weighted least absolute deviation which is not sensitive to leverage points. Its implementation is easy and the computation time is reasonably low. Numerical results give the data structure and the outlying information.

• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 1993년도 한국자동제어학술회의논문집(국내학술편); Seoul National University, Seoul; 20-22 Oct. 1993
• /
• pp.482-485
• /
• 1993

This paper deals with structured singular value and mixed sensitivity problem for robust performance. We derive the sufficient condition that mixed sensitivity problem satisfies structured singular value in robust performance problem. And we show the bound of perturbation between structured singular value and norm of mixed sensitivity functions.

• 한국멀티미디어학회논문지
• /
• 제12권6호
• /
• pp.785-793
• /
• 2009

This paper proposes a signature using dominant singular values for video sequence matching. By considering the input image as matrix A, a partition procedure is first performed to separate the matrix into non-overlapping sub-images of a fixed size. The SVD(Singular Value Decomposition) process decomposes matrix A into a singular value-singular vector factorization. As a result, singular values are obtained for each sub-image, then k dominant singular values which are sufficient to discriminate between different images and are robust to image size variation, are chosen and normalized as the signature for each block in an image frame for matching between the reference video clip and the query one. Experimental results show that the proposed video signature has a better performance than ordinal signature in ROC curve.

• 대한수학회지
• /
• 제37권5호
• /
• pp.823-833
• /
• 2000

In this paper, we develop the method of quasilinearization comvined with the methos of upper and lower solutions for singular second order boundary value problems in weighted spaces. The sequences constructed converge uniformly and monotonically to the unique of the second singular order boundary value problem. Further we prove the rate of convergence is quadratic.

• 대한전기학회:학술대회논문집
• /
• 대한전기학회 2011년도 제42회 하계학술대회
• /
• pp.49-50
• /
• 2011

본 논문에서는 WT(Wavelet Transform)와 SVD(Singular Value Decomposition)를 함께 사용한 WSVD(Wavelet Singular Value Decomposition)를 이용하여 발전기 탈락 시의 전압 변동 특성을 분석하였다. WSVD 특성 분석을 위해 부산 지역의 345kV급 송전계통을 EMTP-RV로 모델링하였으며, 이 계통모델에서 발전기 탈락을 모의하였다. MATLAB을 통해 이 때 측정된 전압의 WSVD를 계산하여 발전기 탈락에 따른 특성을 분석하였다.

• Journal of applied mathematics & informatics
• /
• 제27권5_6호
• /
• pp.1361-1370
• /
• 2009

In this paper, we consider singular fourth-order two point boundary value problems $u^{(4)}$ (t) = f(t, u), 0 < t < 1, u(0) = u(l) = u'(0) = u'(l) = 0, where $f:(0,1){\times}(0,+{\infty}){\rightarrow}[0,+{\infty})$ may be singular at t = 0, 1 and u = 0. By using the upper and lower solution method, we obtained the existence of positive solutions to the above boundary value problems. An example is also given to illustrate the obtained theorems.

• Journal of the Korean Data and Information Science Society
• /
• 제9권1호
• /
• pp.63-70
• /
• 1998

The singular value decomposition is a tool which is used to find a linear structure of reduced dimension and to give interpretation of the lower dimensional structure about multivariate data. In this paper the singular value decomposition is reviewed from both algebraic and geometric point of view and, is illustrated the way which the tool is used in the multivariate techniques finding a simpler geometric structure for the data.

• 한국음향학회지
• /
• 제20권8호
• /
• pp.3-11
• /
• 2001

본 연구에서는 SVD (Singular Value Decomposition)를 이용하여 다중입력과 다중출력을 가지는 시스템에서의 입력을 알아내기 위해 역변환 필터를 구현하였다. SISO (Single-Input and Single-Output)시스템의 입력과 출력의 관계에 대한 행렬공식화 작업을 확장하여 MIMO (Multi-Input and Multi-Output)시스템에 적용하였다. 그리고 시간영역과 주파수영역에서 최소위상 (Minimum phase)시스템과 비최소위상 (Non-minimum phase)시스템에 대한 그 역벽환에 대해 알아보았으며 비최소 위상요소에 대한 효과적인 역변환을 위해 SVD를 도입하였다. 먼저 전체시스템 행렬의 특이값 (singular value)을 계산하고 시스템의 위상에 대해 알아본다. 전체시스템이 비최소 위상인 경우 하나 이상의 매우 작은 특이값을 가지며 이는 시스템의 최소 위상/비최소 위상에 대한 정보를 가짐을 알 수 있다. 이를 이용하여 전체시스템에 대한 근사적인 역변환 필터를 구할 수 있으며 보다 근사적인 역변환 필터를 얻기 위하여 특이벡터를 이용하여 근사적인 역변환 필터를 얻었다. 수치적 예는 이러한 역변환 필터 행렬의 이용에 대한 잠재성을 보여준다.

• 디지털산업정보학회논문지
• /
• 제8권4호
• /
• pp.115-120
• /
• 2012

In multi-user multi-input multi-output (MU-MIMO) system, zero forcing beamforming (ZFB) is regarded as a realistic solution for transmitting scheme due to its low complexity and simple structure. However, ZFB shows a significant performance degradation when channel matrix has large condition number. In this case, the largest singular value of the channel inversion matrix has a dominant effect on transmit power. In this paper, we propose a perturbation method for reducing an effect of the dominant singular value. In the proposed algorithm, channel inverse matrix is first decomposed by SVD for the transmit signal to be expressed as a combination of singular vectors. Then, the transmit signal is perturbed to reduce the coefficient of the singular vector corresponding to the largest singular value. When a number of transmit antennas is 4, the simulation results of this paper shows that the proposed method shows 8dB performance enhancement at 10-3 uncoded bit error rate (BER) compared with conventional ZFB. Also, the simulation results show that the proposed method provides a comparable performance to Tomlinson-Harashima Precoding (THP) with much lower complexity.