• Honam Mathematical Journal
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• v.34 no.2
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• pp.219-230
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• 2012

In the paper, a symbolic construction is considered to define generalized Cantor-like sets. Lower and upper bounds for the correlation dimension of the sets with a regular condition are obtained with respect to a probability Borel measure. Especially, for some special cases of the sets, the exact formulas of the correlation dimension are established and we show that the correlation dimension and the Hausdorff dimension of some of them are the same. Finally, we find a condition which guarantees the positive correlation dimension of the generalized Cantor-like sets.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2006.05a
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• pp.61-64
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• 2006

Based on the geometrical representation of a generalized intuitionistic fuzzy set, we take into account all three parameters describing generalized intuitionistic fuzzy set, propose a method to calculate the correlation coefficient for generalized intuitionistic fuzzy sets in finite set and probability space, respectively, and discuss some properties of correlation and correlation coefficient of generalized intuitionistic fuzzy sets.

• 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.

• Journal of the Korean Statistical Society
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• v.35 no.2
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• pp.143-156
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• 2006

In the present paper, various solutions for generalized canonical correlation analysis (GCCA) are considered depending on the criteria and constraints. For the comparisons of some characteristics of the solutions, we provide with certain unifying stationary equations which might to also useful to obtain various generalized canonical correlation analysis solutions. In addition, we suggest an approach for the generalized canonical correlation analysis by exploiting the concept of maximum eccentricity originally de-signed to test the internal independence structure. The solutions, including new one, are compared through unifying stationary equations and by using some numerical illustrations. A type of iterative procedure for the GCCA solutions is suggested and some numerical examples are provided to illustrate several GCCA methods.

• Honam Mathematical Journal
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• v.28 no.3
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• pp.317-326
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• 2006

Based on the geometrical representation of a generalized intuitionistic fuzzy set, we take into account all three parameters describing generalized intuitionistic fuzzy set and propose new methods to calculate the correlation coefficient for generalized intuitionistic fuzzy sets by means of mathematical statistics.

• 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.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.15 no.9
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• pp.744-750
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• 2003

The performance of adiabatic capillary tubes are measured to provide the database for a generalized correlation. Test conditions and capillary tube geometries are selected to cover a wide range typically observed in air-conditioning and heat pump applications. Based on extensive experimental data for R22, R290, and R407C measured in this study, a generalized correlation for refrigerant flow rate in adiabatic capillary tubes is developed by implementing dimensionless parameters for tube inlet conditions, capillary tube geometry, and refrigerant properties. The correlation yields good agreement with the present data for R22, R290, and R407C with average and standard deviations of 0.9% and 5.0%, respectively. In addition, approximately 97% of the data for Rl2, R134a, R152a, R410A, and R600a obtained in the open literature are correlated within a relative deviation of $\pm$ 15%.

• Journal of the Korean Statistical Society
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• v.31 no.2
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• pp.163-175
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• 2002

An extended version of the minimax eccentricity factor estimation for multiple set case is proposed. In addition, two more simple methods for multiple set factor analysis exploiting the concept of generalized canonical correlation analysis is suggested. Finally, a certain connection between the generalized canonical correlation analysis and the multiple set factor analysis is derived which helps us clarify the relationship.

• The Korean Journal of Applied Statistics
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• v.14 no.1
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• pp.81-90
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• 2001

One of the Repeated survey which estimates variability of population, we can be consider rotation sample survey. There are two kinds of rotation sample survey - onelevel rotation sample survey and multi-level rotation sample survey. In rotation sample survey, Composite estimator is used to measure level or level change of the population. This study suggests Generalized Composite estimator as considering intraclass correlation in multi-level rotation sample survey, and optimal weight minimizing variance of estimator. Numerical example shows efficiency of Generalized Composite estimator as considering intraclass correlation according to the sample unit and change degree of intraclass correlation in the rotation group.

• Genomics & Informatics
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• v.16 no.4
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• pp.33.1-33.9
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• 2018

Recently, there have been many studies in medicine related to genetic analysis. Many genetic studies have been performed to find genes associated with complex diseases. To find out how genes are related to disease, we need to understand not only the simple relationship of genotypes but also the way they are related to phenotype. Multi-block data, which is a summation form of variable sets, is used for enhancing the analysis of the relationships of different blocks. By identifying relationships through a multi-block data form, we can understand the association between the blocks in comprehending the correlation between them. Several statistical analysis methods have been developed to understand the relationship between multi-block data. In this paper, we will use generalized canonical correlation methodology to analyze multi-block data from the Korean Association Resource project, which has a combination of single nucleotide polymorphism blocks, phenotype blocks, and disease blocks.