• The Korean Journal of Applied Statistics
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• v.23 no.5
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• pp.955-966
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• 2010

Canonical correlation biplot is a useful biplot for giving a graphical description of the data matrix which consists of the association between two sets of variables, for detecting patterns and displaying results found by more formal methods of analysis. Nevertheless, when some values are missing in data, most biplots are not directly applicable. To solve this problem, we estimate the missing data using the median, mean, EM algorithm and MCMC imputation methods according to missing rates. Even though we estimate the missing values of biplot of incomplete data, we have different shapes of biplots according to the imputation methods and missing rates. Therefore we use a RMS(root mean square) which was proposed by Shin et al. (2007) and PS(procrustes statistic) for measuring and comparing the shape variability between the original biplots and the estimated biplots.

• Communications for Statistical Applications and Methods
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• v.19 no.1
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• pp.97-105
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• 2012

The generalized canonical correlation biplot is a 2-dimensional plot to graphically investigate the relationship between more than three sets of variables and the relationship between observations and variables. Recently, Choi and Choi (2010) investigated the relationship physique, physical fitness and basic skill factors of Korea Tennis Association(KTA) players of using this biplot; however we consider the set of covariate variables affecting the linearly on two sets of variables. In this case, if we apply the generalized canonical correlation biplot, we cannot clearly interpret the other two sets of variables due to the effect of the set of covariate variables. Moreover, Yeom and Choi (2011) provided partial canonical correlation analysis that removed the linear effect of the set of covariate variables on two sets of variables. In addition, Procrustes analysis is a useful tool for comparing shape between configurations. In this study, we will investigate the relationship between physical fitness and basic skill factors of KTA players of using a partial canonical correlation biplot and Procrustes analysis. We compare shapes and shape variabilities for the generalized, partial and simple canonical correlation biplots.

• Journal of Korea Water Resources Association
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• v.41 no.5
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• pp.517-525
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• 2008

Regional rainfall quantile depends on the identification of hydrologically homogeneous regions. Various variables relevant to precipitation can be used to form regions. Since the type and number of variables may lead to improve the efficiency of partitioning, it is important to select those precipitation related variables, which represent most of the information from all candidate variables. Multivariate analysis techniques can be used for this purpose. Procrustes analysis which can decrease the dimension of variables based on their correlations, are applied in this study. 42 rainfall related variables are decreased into 21 ones by Procrustes analysis. Factor analysis is applied to those selected variables and then 5 factors are extracted. Fuzzy-c means technique classifies 68 stations into 6 regions. As a result, the GEV distributions are fitted to 6 regions while the lognormal and generalized logistic distributions are fitted to 5 regions. For the comparison purpose with previous results, rainfall quantiles based on generalized logistic distribution are estimated by at-site frequency analysis, index flood method, and regional shape estimation method.

• The Korean Journal of Applied Statistics
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• v.25 no.3
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• pp.521-529
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• 2012

Simple canonical correlation biplot is a graphical method to investigate two sets of variables and observations in simple canonical correlation analysis. If we consider the set of covariate variables that linearly affects two sets of variables, we can apply the partial canonical correlation biplot in partial canonical correlation analysis that removes the linear effect of the set of covariate variables on two sets of variables. On the other hand, we consider the set of covariate variables that linearly affect one set of variables but not the other. In this case, if we apply the simple or partial canonical correlation biplot, we cannot clearly interpret other two sets of variables. Therefore, in this study, we will apply the semi-partial canonical correlation analysis of Timm (2002) and remove the linear effect of the set of covariate variables on one set of variables but not the other. And we suggest the semi-partial canonical correlation biplot for interpreting the semi-partial canonical correlation analysis. In addition, we will compare shapes and shape the variabilities of the simple, partial and semi-partial canonical correlation biplots using a procrustes analysis.

• The Korean Journal of Applied Statistics
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• v.23 no.2
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• pp.317-323
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• 2010

Measures are very useful tools for comparing the shape variability in statistical shape analysis. For examples, the Procrustes statistic(PS) is isolated measure, and the mean Procrustes statistic(MPS) and the root mean square measure(RMS) are overall measures. But these measures are very subjective, complicated and moreover these measures are not statistical for comparing the shape variability. Therefore we need to study some tests. It is well known that the Hotelling's $T^2$ test is used for testing shape variability of two independent samples. And for testing shape variabilities of several independent samples, instead of the Hotelling's $T^2$ test, one way analysis of variance(ANOVA) can be applied. In fact, this one way ANOVA is based on the balanced samples of equal size which is called as BANOVA. However, If we have unbalanced samples with unequal size, we can not use BANOVA. Therefore we propose the unbalanced analysis of variance(UNBANOVA) for testing shape variabilities of several independent samples of unequal size.

• Proceedings of the Korea Water Resources Association Conference
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• 2007.05a
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• pp.1568-1572
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• 2007

지역빈도해석은 우리나라와 같이 자료 기간이 짧은 경우 지점빈도해석보다 더 정확한 확률강우량을 산정할 수 있는 기법이다. 지역빈도해석을 통한 확률강우량 산정 결과는 수문학적으로 동질한 지역의 구분 결과에 따라 달라진다. 지역을 구분할 때에는 강우에 영향을 미치는 다양한 변수들이 사용될 수 있다. 변수의 유형과 개수가 지역 구분의 효율성을 좌우하기 때문에 활용 가능한 모든 변수들의 정보를 요약할 수 있는 변수들을 선택하는 것이 지역 구분의 효율성 면에서 유리하다고 할 수 있다. 이런 면에서 지역 구분의 효율성을 증대시킬 목적으로 다변량 분석 기법이 활용될 수 있다. 본 연구에서는 주성분 분석, 요인 분석, Procrustes analysis와 같은 다변량 분석 기법을 활용하여 42개의 강우 관련 변수들을 33개의 변수로 줄일 수 있었다. 분석 결과 변수 개수 감소로 인한 정보 손실은 크지 않은 것으로 나타났다. 따라서 이러한 기법에 의한 변수 차원의 축소는 지역 구분의 효율성 향상에 기여할 수 있는 것으로 판단된다. 선정된 변수들을 바탕으로 군집해석을 수행하여 지역을 구분하였고, L-모멘트에 근거한 이질성척도(H)를 활용하여 구분된 지역의 동질성을 검토하였다. 또한 L-모멘트에 근거한 적합성 척도(Z)를 적용하여 구분된 지역에 적합한 확률분포형을 선정하였고, 선정된 적정 확률분포형을 바탕으로 각 지역에 대한 성장 곡선(growth curve)을 유도하였다.

• Journal of Institute of Control, Robotics and Systems
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• v.20 no.10
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• pp.1044-1050
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• 2014

Robots used for pipe inspection have been studied for a long time and many mobile mechanisms have been proposed to achieve inspection tasks within pipelines. Localization is an important factor for an inpipe robot to perform successful autonomous operation. However, sensors such as GPS and beacons cannot be used because of the unique characteristics of inpipe conditions. In this paper, an inpipe localization algorithm based on elbow detection is presented. By processing the projected marker images of laser pointers and the attitude and heading data from an IMU, the odometer module of the robot determines whether the robot is within a straight pipe or an elbow and minimizes the integration error in the orientation. In addition, an off-line positioning algorithm has been performed with forward and backward estimation and Procrustes analysis. The experimental environment has consisted of several straight pipes and elbows, and a map of the pipeline has been constructed as the result.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.38 no.4
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• pp.305-315
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• 2020

The purpose of this study is to compare algorithms of single photo resection, which determines the exterior orientation parameters used in fields such as photogrammetry, computer vision, robotics, etc. To this end, the algorithms were compared by generating experimental data by simulating terrain based on a camera used in aerial and close-range photogrammetry. Through experiments on aerial photographic camera that was taken almost vertically, it was possible to determine the exterior orientation parameters using three ground control points, but the Procrustes algorithm was sensitive to the configuration of the ground control points. Even in experiments with a close-range amateur camera where the attitude angles of the camera change significantly, the algorithm was sensitive to the configuration of the ground control points, and the other algorithms required at least six ground control points. Through experiments with two types of cameras, it was found that cosine lawbased spatial resection shows performance similar to that of a traditional photogrammetry algorithm because the number of iterations is short and no explicit initial values are required.

• Imaging Science in Dentistry
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• v.51 no.2
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• pp.167-174
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• 2021

Purpose: Sex determination can be done by morphological analysis of different parts of the body. The mastoid region, with its anatomical location at the skull base, is ideal for sex identification. Statistical shape analysis provides a simultaneous comparison of geometric information on different shapes in terms of size and shape features. This study aimed to investigate the geometric morphometry of the inter-mastoid triangle as a tool for sex determination in the Iranian population. Materials and Methods: The coordinates of 5 landmarks on the mastoid process on the 80 cone-beam computed tomographic images(from individuals aged 17-70 years, 52.5% female) were registered and digitalized. The Cartesian x-y coordinates were acquired for all landmarks, and the shape information was extracted from the principal component scores of generalized Procrustes fit. The t-test was used to compare centroid size. Cross-validated discriminant analysis was used for sex determination. The significance level for all tests was set at 0.05. Results: There was a significant difference in the mastoid size and shape between males and females(P<0.05). The first 2 components of the Procrustes shape coordinates explained 91.3% of the shape variation between the sexes. The accuracy of the discriminant model for sex determination was 88.8%. Conclusion: The application of morphometric geometric techniques will significantly impact forensic studies by providing a comprehensive analysis of differences in biological forms. The results demonstrated that statistical shape analysis can be used as a powerful tool for sex determination based on a morphometric analysis of the inter-mastoid triangle.

• The Korean Journal of Applied Statistics
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• v.37 no.1
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• pp.73-86
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• 2024

A radial chart of Excel is very useful graphical method in delivering information for numerical data. However, it is not easy to discriminate or classify many individuals. In this case, after shaping each individual of a radial chart, we need to apply shape analysis. For a radial chart, since landmarks for shaping are formed as many as the number of variables representing the characteristics of the object, we consider a shape that connects them to a line. If the shape becomes complicated due to the large number of variables, it is difficult to easily grasp even if visualized using a radial chart. Principal component analysis (PCA) is performed on variables to create a visually effective shape. The classification table and classification rate are checked by applying the techniques of traditional discriminant analysis, support vector machine (SVM), and artificial neural network (ANN), before and after principal component analysis. In addition, the difference in discrimination between the two coordinates of generalized procrustes analysis (GPA) coordinates and Bookstein coordinates is compared. Bookstein coordinates are obtained by converting the position, rotation, and scale of the shape around the base landmarks, and show higher rate than GPA coordinates for the classification rate.