대응분석에서 상호평균법 활용에 대한 소고

김대학,정형철 한국자료분석학회 2013 Journal of the Korean Data Analysis Society Vol.15 No.6

Correspondence analysis is a statistical technique which project the rows and columns of contingency tables into lower dimension. It is conceptually similar to principal component analysis and widely applicable method to many areas. Benzecri (1973) considered correspondence analysis as an weighted principal component analysis. Hayashi considered correspondence analysis as a canonical correlation analysis. Both methods depend on the singular value decomposition and lead the same solution. On the while, reciprocal averaging method uses reconstitution formula based on numerical analysis and gives different solution from correspondence analysis or quantification method. In this paper, we introduce correspondence analysis, quantification and reciprocal averaging, respectively and investigate the properties of reciprocal averaging method. Scale change is also considered for the application of reciprocal averaging based on the result of correspondence analysis or quantification method. This is meaningful in the sense of re-quantification of result of correspondence analysis. 대응분석은 범주형자료의 행과 열을 낮은 차원에 사영하는 방법으로 활용성이 높은 통계적 방법이다. 저차원 공간 사영에 대해, Benzecri(1973)의 대응분석은 가중주성분분석으로, 수량화 3법은 정준상관분석으로 접근한다. 그런데 두 방법 모두 특이치 분해에 의존하며 동일한 해를 유도하는 특징을 지닌다. 반면, 상호평균법(reciprocal averaging)은 재형성 공식을 활용하는 수치해석 방법으로 대응분석의 해와 차이가 있다. 본 논문에서는 대응분석, 수량화 3법, 상호평균법 등의 방법론을 간략히 소개하고, 그 특징을 살펴보았다. 또한, 대응분석의 결과를 0~100 점 규모로 변경하기 위해, 대응분석이나 수량화 3의 결과를 초기값으로 사용하여, 상호평균법 알고리즘을 구동할 수 있음을 제시하였다. 이는 대응분석 결과를 재수량화 한다는 점에서 의의를 지닌다.

Forward Kinematic Singularity Avoiding Design of a Schönflies Motion Generator by Asymmetric Attachment of Subchains

김성목,이병주,김희국 제어·로봇·시스템학회 2013 International Journal of Control, Automation, and Vol.11 No.1

In most of the previous studies on parallel mechanisms (PMs), architectural design mainly relying on symmetric geometry was investigated without in-depth analysis of its performance. This work demonstrates that such a symmetric geometry of multiple subchains sometimes induces a forward kinematic singularity which degrades the overall kinematic performance of PMs within the desired workspace and claims that an asymmetric attachment of those subchains on a moving platform can effectively resolve such a singularity problem. A 4-Degree-of-Freedom (DOF) PM exhibiting Schönflies motions is examined as an example device. First, its mobility analysis and kinematic modeling via screw theory are conducted. Then a singularity analysis based on Grassmann line geometric conditions is carried out, and the forward kinematic singularities of the mechanism are identified and verified by simulations. Based on these analysis and simulations, a forward kinematic singularity-free design is suggested. To show the high potential of the device in practical applications, its output stiffness and dynamic motion capability are examined. Then a prototype is built and its motions capability is verified through experiments.

부채널 분석 성능향상을 위한 특이값분해 신호처리 기법에 관한 연구

박건민(Geonmin Bak),김태원(Taewon Kim),김희석(HeeSeok Kim),홍석희(Seokhie Hong) 한국정보보호학회 2016 정보보호학회논문지 Vol.26 No.6

부채널 분석에서 신호처리 기법은 차원 압축이나 잡음 제거를 통해 분석의 효율성과 성능을 높일 수 있는 전처리 기법이다. 특이값 분해를 이용한 신호처리 방법은 신호의 분산 정보나 경향성 등을 이용하여 주 신호 정보를 높이고 잡음신호를 낮출 수 있어, 분석 성능 향상에 큰 도움이 된다. 대표적인 기법은 주성분분석과 선형판별분석 그리고 Singular Spectrum Analysis(SSA)가 있다. 주성분분석과 선형판별분석은 주 신호의 정보를 집약하여 차원 압축을 할 수 있으며, SSA는 본 신호를 주 신호와 잡음 신호로 분해하여 잡음 제거가 가능하다. 세 가지 기법 각각을 사용하거나 조합하여 사용할 경우 성능적인 측면을 비교할 필요가 있으며, 그에 대한 방법론이 필요하다. 본 논문에서는 세 기법을 개별적으로 사용할 경우와 조합하여 사용할 경우의 성능을 비교 분석하였으며, 신호 대 잡음비를 이용한 비교분석 방법론을 제시하였다. 제시한 방법론과 다양한 비교분석 실험을 통해 각 기법의 성능과 효율성을 확인하였다. 이로 인해 부채널 분석 분야의 많은 연구자들에게 유용한 정보를 제공할 것이다. 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.

가중주성분분석을 활용한 정준대응분석과 \\ 가우시안 반응 모형에 의한 정준대응분석의 동일성 연구

정형철 한국통계학회 2021 응용통계연구 Vol.34 No.6

In this study, we considered the algorithm of Legendre and Legendre (2012), which derives canonical correspondence analysis from weighted principal component analysis. And, it was proved that the canonical correspondence analysis based on the weighted principal component analysis is exactly the same as Ter Braak's (1986) canonical correspondence analysis based on the Gaussian response model. Ter Braak (1986)'s canonical correspondence analysis derived from a Gaussian response curve that can explain the abundance of species in ecology well uses the basic assumption of the species packing model and then conducts generalized linear model and canonical correlation analysis. It is derived by way of binding. However, the algorithm of Legendre and Legendre (2012) is calculated in a method quite similar to Benzecri's correspondence analysis without such assumptions. Therefore, if canonical correspondence analysis based on weighted principal component analysis is used, it is possible to have some flexibility in using the results. In conclusion, this study shows that the two methods starting from different models have the same site scores, species scores, and species-environment correlations. 본 연구에서는 가중주성분분석으로부터 정준대응분석을 유도하는 Legendre와 Legendre (2012)의 알고리즘을 고찰하였다. 그리고, 가중주성분분석에 기반한 Legendre와 Legendre (2012)의 정준대응분석이 가우시안 반응모형에 기초한 Ter Braak (1986)의 정준대응분석과 동일함을 다루었다. 생태학에서 종의 발현 정도를 잘 설명할 수 있는 가우시안 반응곡선에서 도출된 Ter Braak (1986)의 정준대응분석은 종 패킹 모형(species packing model)이라는 기본 가정을 사용한 후 일반화선형모형과 정준상관분석을 결합시키는 방법으로 도출된다. 그런데 Legendre와 Legendre (2012)의 알고리즘은 이러한 가정없이 Benzecri의 대응분석과 상당히 유사한 방법으로 계산되는 특징을 지닌다. 그러므로 가중주성분석에 기초한 정준대응분석을 사용하면, 결과물 활용에 약간의 유연성을 지닐 수 있게 된다. 결론적으로 본 연구에서는 서로 다른 모형에서 출발한 두 방법이 장소점수(site score), 종 점수(species score) 그리고 환경변수와의 상관관계가 서로 동일함을 보인다.

세 물체 간 마찰 완전 접촉 문제의 응력 특이성 거동

김형규 한국트라이볼로지학회 2019 한국윤활학회지(윤활학회지) Vol.35 No.4

This study investigates the stress singularity that occurs at the contact edge of three bodies in a frictional complete contact. We use the asymptotic analysis method, wherein we constitute an eigenvalue problem and observe the eigenvalue behavior, which we use to obtain the order of the stress singularity. For the present geometry of three bodies in contact, a contact between a cracked indenter and half plane is considered. This is a typical geometry of the PCMI problem of a nuclear fuel rod. Thus, this paper, specifically presents the characteristics of the PCMI problem from the perspective of stress singularity. Consequently, it is noted that the behavior of the stress singularity varies with the difference in the crack angle, coefficient of friction, and material dissimilarity, as is observed in a frictional complete contact of two bodies. In addition, we find that the stress singularity changes essentially linearly with respect to the coefficient of friction, regardless of the variation in the crack angle and material dissimilarity. Concurrently, we find the order of singularity to be 0.5 at a certain coefficient of friction, irrespective of the crack angle, which we also observe in the crack problem of a homogeneous and isotropic body. The order of singularity can also exceed 0.5 in the frictional complete contact problem of three bodies. This implies that the propensity for failure when three bodies are in frictional complete contact can be even worse than that in case of a failure induced by a crack.

Resistant Singular Value Decomposition and Its Statistical Applications

Park, Yong-Seok,Huh, Myung-Hoe The Korean Statistical Society 1996 Journal of the Korean Statistical Society Vol.25 No.1

The singular value decomposition is one of the most useful methods in the area of matrix computation. It gives dimension reduction which is the centeral idea in many multivariate analyses. But this method is not resistant, i.e., it is very sensitive to small changes in the input data. In this article, we derive the resistant version of singular value decomposition for principal component analysis. And we give its statistical applications to biplot which is similar to principal component analysis in aspects of the dimension reduction of an n x p data matrix. Therefore, we derive the resistant principal component analysis and biplot based on the resistant singular value decomposition. They provide graphical multivariate data analyses relatively little influenced by outlying observations.

Resistant Principal Factor Analysis

Park, Youg-Seok,Byun, Ho-Seon The Korean Statistical Society 1996 Journal of the Korean Statistical Society Vol.25 No.1

Factor analysis is a multivariate technique for describing the in-terrelationship among many variables in terms of a few underlying but unobservable random variables called factors. There are various approaches for this factor analysis. In particular, principal factor analysis is one of the most popular methods. This follows the mathematical algorithm of the principal component analysis based on the singular value decomposition. But it is known that the singular value decomposition is not resistant, i.e., it is very sensitive to small changes in the input data. In this article, using the resistant singular value decomposition of Choi and Huh (1994), we derive a resistant principal factor analysis relatively little influenced by notable observations.

Sensitivity analysis for ranked data

한상태 한국통계학회 2014 Journal of the Korean Statistical Society Vol.43 No.1

Sensitivity analysis is to study the influence of a small change in the input data on theoutput of the analysis. Han and Huh (1995) developed a quantification method for theranked data. However, the question of stability in the analysis of ranked data has not beenconsidered. Here, we propose a method of sensitivity analysis for ranked data. Our aim is toevaluate perturbations by using a graphical approach suggested by Han and Huh (1995). Itextends the results obtained by Tanaka (1984) and Huh (1989) for the sensitivity analysis inHayashi’s third method of quantification and those by Huh and Park (1990) for the principalcomponent reduction of the case influence derivatives in regression. A numerical exampleis provided to explain how to conduct sensitivity analysis based on the proposed approach.

Robust Simple Correspondence Analysis

Park, Yong-Seok,Huh, Myung-Hoe The Korean Statistical Society 1999 Journal of the Korean Statistical Society Vol.28 No.3

Simple correspondence analysis is a technique for giving a joint display of points representing both the rows and columns of an n$\times$p two-way contigency table. In simple correspondence analysis, the singular value decomposition is the main algebraic tool. But, Choi and Huh(1996) pointed out the singular value decomposition is not robust. Instead, they developed a robust singular value decomposition and provided applications in principal component analysis and biplots. In this article, by using the analogous procedures of Choi and Huh(1996), we derive a robust version of simple correspondence analysis.

Projection spectral analysis: A unified approach to PCA and ICA with incremental learning

강훈,이현수 한국전자통신연구원 2018 ETRI Journal Vol.40 No.5

Projection spectral analysis is investigated and refined in this paper, in order to unify principal component analysis and independent component analysis. Singular value decomposition and spectral theorems are applied to nonsymmetric correlation or covariance matrices with multiplicities or singularities, where projections and nilpotents are obtained. Therefore, the suggested approach not only utilizes a sum‐product of orthogonal projection operators and real distinct eigenvalues for squared singular values, but also reduces the dimension of correlation or covariance if there are multiple zero eigenvalues. Moreover, incremental learning strategies of projection spectral analysis are also suggested to improve the performance.