• 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.24 no.3
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• pp.559-566
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• 2011

Biplot is a useful graphical method to explore simultaneously rows and columns of two-way data matrix. In particular, canonical correlation biplot is a method for investigating two sets of variables and observations in canonical correlation analysis graphically. For more than three sets of variables, we can apply the generalized canonical correlation biplot in generalized canonical correlation analysis which is an expansion of the canonical correlation analysis. On the other hand, we consider the set of covariate variables which is affecting the linearly 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. Therefor, in this paper, we will apply the partial canonical correlation analysis of Rao (1969) removing the linear effect of the set of covariate variables on two sets of variables. We will suggest the partial canonical correlation biplot for inpreting the partial canonical correlation analysis graphically.

• The Korean Journal of Ecology
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• v.9 no.3
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• pp.135-147
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• 1986

The simplification and the searching trends of complex data which assumed relationship between predictor variables and object variables are one of primary objective of ecological research. This study was aimed to apply cononical analysis consisting of canonical correlation analysis and canonical variate analysis related to lichen vegetation and several environmental variables which are elevation, height on grond, exposure side and cover values. Data collected from the Duckyoo National Park in August 1985. Lichen species was ranked by eqivocation information theory with cover values. Canonical correlation analysis was applied to one data set both set both environmental variables and lichem family. In order to make two sets of data matrix the scale of position vector ordination was calculated from the vector scalar product for lichen species. Canonical variate analysis was applied to rearranged data which was made by interval class code for environmental variables. The sharpness values was calculated in frequency of cotingency tables and the dispersion profiles of each species in classes of environmental variables was designed to extract component values based on the decomposition of expected frequencies in contingency table. The results of canonical correlation analysis revealed canonical first correlation value 0.815(89%), and second correlation value 0.083(11%). Significance test showed that the hypothesis of joint mutuallity of canonical correlation is accepted (P>0.05). The relation between canonical score of vegetation variables and that of environmental variable indicated linear tendency.

• Bulletin of the Korean Chemical Society
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• v.25 no.2
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• pp.285-288
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• 2004

A canonical transformation changes variables such as coordinates and momenta to new variables preserving either the Poisson bracket or the commutation relations depending on whether the problem is classical or quantal respectively. Classically canonical transformations are well established as a powerful tool for solving differential equations. Quantum canonical transformations have been defined and used relatively recently because of the non-commutativeness of the quantum variables. Three elementary canonical transformations and their composite transformations have quantum implementations. Quantum canonical transformations have been mostly used in time-independent Schrodinger equations and a harmonic oscillator with time-dependent angular frequency is probably the only time-dependent problem solved by these transformations. In this work, we apply quantum canonical transformations to a harmonic oscillator in which both angular frequency and equilibrium position are time-dependent.

• Communications for Statistical Applications and Methods
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• v.26 no.3
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• pp.305-313
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• 2019

Generalized canonical correlation analysis (GCCA) extends the canonical correlation analysis (CCA) to the case of more than two sets of variables and there have been many studies on how two-set canonical solutions can be generalized. In this paper, we derive certain stationary equations which can lead the higher-order solutions of several GCCA methods and suggest a type of iterative procedure to obtain the canonical coefficients. In addition, with some numerical examples we present the methods for graphical display, which are useful to interpret the GCCA results obtained.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.41 no.8
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• pp.902-913
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• 1992

There have been several control schemes for the single input systems with unmeasurable state variables using variable structure control(VSC) theory. In the previous VSC, the systems must be represented in phase canonical form and the complete measurements for each state variable must be assumed. In order to eliminate these restrictions several VSC methods were proposed. And especially for the systems in phase canonical form with unmeasurable state variables, the reduced order switching function algorithm was proposed. But this method has many drawbacks and can not be used in the case of general form (not phase canonical form) dynamic system. Therefore this paper propose new construction method of switching fuction for the systems in phase canonical form, which reduce the restriction of reduced order switching function algorithm. And this algorithm can be realized for any state representation and adopted in the systems where not all states are available for switching function synthesis or control.

• Journal of Korean Society of Forest Science
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• v.79 no.1
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• pp.16-20
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• 1990

Canonical correlation analysis was used to relate 17 soil-site variables to bamboo diameter, height, and internodal characteristics. The first canonical correlation was highly significant, explained much of the variance in both sets of variables, and the canonical variates made sense biologically. Surface soil depth, total nitrogen and percent organic matter had high positive correlations with the first soil-site canonical variate. Clay content (%) and cation exchange capacity were negatively correlated with the first soil-site canonical variate. Only 8 of predictor variables were considered relevant for predicting bamboo growth.

• Journal of the Korean Data and Information Science Society
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• v.15 no.3
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• pp.515-521
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• 2004

Categorical data are mostly found in oriental medical research. The nonlinear canonical correlation analysis does not assume an interval level of measurement. In this paper, we apply nonlinear canonical correlation analysis to quantification and explain how similar sets of variables are to one another for paralysis disease data.

• Communications for Statistical Applications and Methods
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• v.17 no.6
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• pp.917-925
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• 2010

The canonical correlation biplot is a 2-dimensional plot for graphically investigating the relationship between two sets of variables and the relationship between observations and variables in the canonical correlation analysis. Recently, Choi and Choi (2008) suggested a method for investigating the relationship between skill and competition score factors of KLPGA players using this biplot. Choi et al. (2010) used this biplot to analyze the player characteristic factors and competitive factors of tennis Grand Slam competition. Moreover, Huh (1999) provided a generalized canonical correlation analysis and biplot for more than three sets of variables. A Procrustes analysis is a useful tool for comparing shapes between configurations. This study will provide a method to investigate the relationship between physique, physical fitness and basic skill factors of tennis players in the Korea Tennis Association using a generalized canonical correlation biplot and Procrustes analysis.

• Journal of the Korean Society of Clothing and Textiles
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• v.29 no.7 s.144
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• pp.959-967
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• 2005

The color of apparels has the interaction of the face skin colors of the wearers. This study was carried out to classify the face skin colors of Korean males into several similar face skin colors in order to extract favorable colors which flatter to their face skin colors. The criterion that select the new subjects who have the classified face skin colors have to be decided. With color spectrometer, JX-777, face skin colors of subjects were measured quantitatively and classified into three clusters that had similar hue, value and chroma with Munsell Color System. Sample size was 418 Korean males and other 15 of new males subjects. Data were analyzed by K-means cluster analysis, ANOVA, Duncan multiple range test, Stepwise discriminant analysis using SPSS Win. 12. Findings were as follows: 1. 418 subjects who have YR colors were clustered into 3 kinds of face skin color groups. 2. Discriminant variables of face skin colors was 4 variables : L value of forehead, v value of cheek, c value of forehead, and b value of cheek from standardized canonical discriminant function coefficient 1 and c value of forehead, L value of forehead, b value of cheek. and L value of cheek from standardized canonical discriminant function coefficient 2. 3. Hit ratio of type 1 was $92.3\%$, of type 2 was $96.5\%$ and of type 3 was $92.6\%$ by the canonical discriminant function of 4 variables. 4. The canonical discriminant function equation 1 and 2 were calculated with the unstandardized canonical discriminant function coefficient and constant, the cutting score, and range of the score were computed. 5. The criterion that select the new subjects who have the classified face skin colors was decided.