• 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.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.9 no.2
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• pp.147-153
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• 2009

In this paper, we introduce several concepts of tightness for a sequence of random variables taking values in the space of normal and upper-semicontinuous fuzzy sets with compact support in $R^p$ and give some characterizations of their concepts. Also, counter-examples for the relationships between the concepts of tightness are given.

• Journal of the Korean Institute of Intelligent Systems
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• v.15 no.3
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• pp.337-342
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• 2005

The present paper establishes the improved version of central limit theorem for sums of level-continuous fuzzy set-valued random variables as a generalization of central limit theorem for sums of independent and identically distributed set-valued random variables.

• 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.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2004.04a
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• pp.385-388
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• 2004

The present paper establish the improved version of central limit theorem for sums of level-continuous fuzzy random variables as a generalization of central limit theorem for sums of independent and identically distributed random sets.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.13 no.3
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• pp.215-223
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• 2013

In this paper, we present some results on weak laws of large numbers for weighted sums of fuzzy random variables taking values in the space of normal and upper-semicontinuous fuzzy sets with compact support in a separable real Banach space. First, we give weak laws of large numbers for weighted sums of strong-compactly uniformly integrable fuzzy random variables. Then, we consider the case that the weighted averages of expectations of fuzzy random variables converge. Finally, weak laws of large numbers for weighted sums of strongly tight or identically distributed fuzzy random variables are obtained as corollaries.

• Korean Journal of Mathematics
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• v.21 no.4
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• pp.383-399
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• 2013

In this paper, we establish two types of strong law of large numbers for fuzzy random variables taking values on the space of normal and upper-semicontinuous fuzzy sets with compact support in a separable Banach space. The first result is SLLN for strong-compactly uniformly integrable fuzzy random variables, and the other is the case of that the averages of its expectations converges.

• The Korean Journal of Applied Statistics
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• v.25 no.1
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• pp.225-237
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• 2012

This study proposes a quantification algorithm for a PLS method with several sets of variables. We called the quantification method for PLS with more than 2 sets of data a generalization. The basis of the quantification for PLS method is singular value decomposition. To derive the form of singular value decomposition in the data with more than 2 sets more easily, we used the constraint, $a^ta+b^tb+c^tc=3$ not $a^ta=1$, $b^tb=1$, and $c^tc=1$, for instance, in the case of 3 data sets. However, to prove that there is no difference, we showed it by the use of 2 data sets case because it is very complicate to prove with 3 data sets. The keys of the study are how to form the singular value decomposition and how to get the coordinates for the plots of variables and observations.

• Journal of the Korean Statistical Society
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• v.25 no.4
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• pp.589-601
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• 1996

Geometric approach to extend the classical two-set theory of canonical correlation analysis to three or more sets is considered. It provides statistical graphs to represent the data in a low dimensional space. Procedures are developed for computing the canonical variables and the corresponding properties are investigated. The solution is equivalent to that of the usual problem in the case of two sets. Goodness-of-fit of the proposed plots is studied and a numerical example is included.

• Physical Therapy Korea
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• v.8 no.3
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• pp.77-95
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• 2001

The purpose of this study was to investigate the effects of resting periods between exercise sets during isokinetic contraction on recovery from muscle fatigue, strength, heart rate, blood pressure, and lactate level. Sixteen women performed 10 repetitions of isokinetic exercise for three sets in three different conditions. During the sets, they rested 50, 100, and 150 seconds in each condition. And the results were: 1) In this population, the peak torque of extensor during the isokinetic exercise in 100 second resting condition was significantly higher than that in 50 and 150 second resting conditions (p<.01). The total work of extensor was significant in the second and third sets in 50 and 100 second resting conditions (p<.01). 2) During the isokinetic exercise, the heart rate was progressively increased as the sets were advanced in all resting conditions (p<.01). And the increase was significant during the second and third sets than the first in 50 second resting condition (p<.01), while it was significantly greater after the third set than the first in 100 and 150 second resting conditions (p<.01). 4) No difference was found between the resting periods in blood lactate level and blood pressure during the isokinetic exercise. However, differences were found between the sets in these variables (p<.01).