• Communications for Statistical Applications and Methods
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• v.12 no.3
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• pp.683-696
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• 2005

The results of using principal coordinates prior to cluster analysis are investigated on the samples from multiple binary outcomes. The retrieval ability of the known clustering algorithm is significantly improved by using principal coordinates instead of using the distance directly transformed from four association coefficients for multiple binary variables.

• Wind and Structures
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• v.7 no.5
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• pp.333-344
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• 2004

This paper illustrates application of the proper orthogonal decomposition (POD) and the autoregressive (AR) model to simulate large wind pressures due to gusts on a low-rise building. In the POD analysis, the covariance of the ensemble of large wind pressures is employed to calculate the principal modes and coordinates. The POD principal coordinates are modeled using the AR process, and the fitted AR models are employed to generate the principal coordinates. The generated principal coordinates are then used to simulate large wind pressures. The results show that the structure characterizing large wind pressures is well represented by the dominant eigenmodes (up to the first fifteen eigenmodes). Also, wind pressures with large peak values are simulated very well using the dominant eigenmodes along with the principal coordinates generated by the AR models.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2011.04a
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• pp.278-281
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• 2011

The global coordinates generated from Isomap algorithm provide a simple way to analyze and manipulate high dimensional observations in terms of their intrinsic nonlinear degrees of freedom. Thus, Isomap can find globally meaningful coordinates and nonlinear structure of complex data sets, while neither principal component analysis (PCA) nor multidimensional scaling (MDS) are successful in many cases. It is demonstrated that the adapted Isomap algorithm successfully enhances the quality of pattern classification for damage identification in various numerical examples.

• Communications for Statistical Applications and Methods
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• v.8 no.3
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• pp.643-650
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• 2001

Some classical plots like scatterplot matrices and parallel coordinates are valuable tools for data visualization. These tools are extensively used in the modern data mining softwares to explore the inherent data structure, and hence to visually classify or cluster the database into appropriate groups. However, the interpretation of these plots are very sensitive to the arrangement of variables. In this work, we introduce two methods to arrange the variables for data visualization. First method is based on the work of Wegman (1999), and this is to arrange the variables using minimum distance among all the pairwise permutation of the variables. Second method is using the idea of principal components. We Investigate the effectiveness of these methods with parallel coordinates using real data sets, and show that each of the two proposed methods has its own strength from different aspects respectively.

• Korean Journal of Applied Biomechanics
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• v.34 no.1
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• pp.34-44
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• 2024

Objective: This study aimed to investigate how the movements occurring during the follow-through phase after releasing an arrow among elite compound archers, are associated with the arrow impact points on the target. Method: Nine elite archers performed consecutive compound archery shooting under conditions identical to actual competitions using their own bows and equipment. Motion capture system and force platform were utilized to record the changes in joint positions and center of pressure, respectively. Principal component analysis was employed to identify the patterns in which multidimensional joint positions and COP changes were organized with horizontal and vertical coordinates of arrow impact points. Subsequently, correlation analysis quantified the relationship between individual variables and the coordinates of arrow impacts on the target. Results: We found a common organizational pattern in which the two axes of the impact point coordinates were grouped into the first two principal components. The movements of the upper and lower limbs following release exhibited opposite patterns in the anterior-posterior axis, with significant correlations observed between the arrow impact points of the horizontal axis and the left shoulder, right elbow, left hip, and both knees. Additionally, the lateral movements induced by the reaction force upon arrow release showed significant associations with the vertical coordinates of the impact points. Particularly, the correlations between the movements of the left shoulder and elbow, as well as the bilateral hip and right knee, were consistently observed among all participants. Conclusion: These findings implied that the post-release movements could significantly influence the trajectory and impact points of the arrows in compound archery. We suggest that a consistent and controlled movement during the follow-through phase may be more beneficial for optimizing shooting accuracy and precision rather than minimizing movements.

• Honam Mathematical Journal
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• v.44 no.2
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• pp.259-270
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• 2022

This paper is devoted to the geometry of vector fields and timelike flows in terms of anholonomic coordinates in three dimensional Lorentzian space. We discuss eight parameters which are related by three partial differential equations. Then, it is seen that the curl of tangent vector field does not include any component in the direction of principal normal vector field. This implies the existence of a surface which contains both s - lines and b - lines. Moreover, we examine a normal congruence of timelike surfaces containing the s - lines and b - lines. Considering the compatibility conditions, we obtain the Gauss-Mainardi-Codazzi equations for this normal congruence of timelike surfaces in the case of the abnormality of normal vector field is zero. Intrinsic geometric properties of these normal congruence of timelike surfaces are obtained. We have dealt with important results on these geometric properties.

• Journal of Advanced Marine Engineering and Technology
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• v.25 no.5
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• pp.1130-1139
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• 2001

Springs are widely utilized in machine element. To find out stiffness of coil spring, the space beam theory using the finite element method is adopted in this paper. In three dimensional space, a space frame element is a straight bar of uniform cross section which is capable of resisting axial forces, bending moments about two principal axes in the plane of its cross section and twisting moment about its centroidal axis. The corresponding displacement degrees of freedom are twelve. The displacements of nodal points due to small increment of force are calculated by the finite element method and the calculated nodal displacements are added to coordinates of nodal points. The new stiffness matrix of the system using the new coordinates of nodal points is adopted to calculated the another increments of nodal displacements, that is, the step by step method is used in this paper. The results of the finite element method are fairly well agreed with those of various experiments. Using MATLAB program developed in this paper, spring constants can be predicted by input of few factors.

• Proceedings of the Korean Society of Marine Engineers Conference
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• 2001.11a
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• pp.21-27
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• 2001

Springs are widely utilized in machine element. To find out stiffness of frustum-shaped coil spring, the space beam theory using the finite element method is adopted in this paper In three dimensional space, a space frame element is a straight bar of uniform cross section which is capable of resisting axial forces, bending moments about two principal axes in the plane of its cross section and twisting moment about its centroidal axis. The corresponding displacement degrees of freedom are twelve. To find out load vector of coil spring subjected to distributed compression, principle of virtual work is adapted The displacements of nodal points due to small increment of force are calculated by the finite element method and the calculated nodal displacements are added to coordinates of nodal points. The new stiffness matrix of the system using the new coordinates of nodal points is adopted to calculate the another increments of nodal displacements, that is, the step by step method is used in this paper. The results of the finite element method are fairly well agreed with those of various experiments. Using MATLAB program developed in this paper, spring constants and stresses can be predicted by input of few factors.

• 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.

• Wind and Structures
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• v.7 no.6
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• pp.373-392
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• 2004

This paper presents a methodology for spatial extrapolation of wind-induced pressure time series from a corner bay to roof locations on a low building away from the corner through the application of proper orthogonal decomposition (POD). The approach is based on the concept that pressure time series in the far field can be approximated as a linear combination of a series of modes and principal coordinates, where the modes are extracted from the full roof pressure field of an aerodynamically similar building and the principal coordinates are calculated from data at the leading corner bay only. The reliability of the extrapolation for uplift time series in nine bays for a cornering wind direction was examined. It is shown that POD can extrapolate reasonably accurately to bays near the leading corner, given the first three modes, but the extrapolation degrades further from the corner bay as the spatial correlations decrease.