• The Korean Journal of Applied Statistics
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• v.19 no.3
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• pp.431-445
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• 2006

In this paper we review some methods for analyzing functional data and illustrate real application of functional data analysis. Representing methods for functional data by using basis function, analyzing functional variation by functional principal component analysis and functional linear models are reviewed. For a real application, we use temperature and precipitation data measured in Korea from the January of 1970 to the May of 2004. We apply functional principal component analysis for each data and test the significance of regional division done by using shining hours. We also estimate functional regression model for temperature and precipitation.

• International Journal of Knowledge Content Development & Technology
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• v.10 no.1
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• pp.7-20
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• 2020

For research data to be shared without legal, financial and technical barriers in the Open Science era, data repositories must have the functional requirements asked by DMP and CoreTrustSeal. In order to derive functional requirements for the data repository, this study analyzed the Data Management Plan (DMP) and CoreTrustSeal, the criteria for certification of research data repositories. Deposit, Ethics, License, Discovery, Identification, Reuse, Security, Preservation, Accessibility, Availability, and (Meta) Data Quality, commonly required by DMP and CoreTrustSeal, were derived as functional requirements that should be implemented first in implementing data repositories. Confidentiality, Integrity, Reliability, Archiving, Technical Infrastructure, Documented Storage Procedure, Organizational Infrastructure, (Meta) Data Evaluation, and Policy functions were further derived from CoreTrustSeal. The functional requirements of the data repository derived from this study may be required as a key function when developing the repository. It is also believed that it could be used as a key item to introduce repository functions to researchers for depositing data.

• The Korean Journal of Applied Statistics
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• v.35 no.5
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• pp.579-591
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• 2022

Functional data is collected in various fields. It is often necessary to test whether there are differences among groups of functional data. In this case, it is not appropriate to explain using the point-wise ANOVA method, and we should present not the point-wise result but the integrated result. Various studies on functional data analysis of variance have been proposed, and recently implemented those methods in the package fdANOVA of R. In this paper, I first explain ANOVA and multivariate ANOVA, then I will introduce various methods of analysis of variance for univariate and multivariate functional data recently proposed. I also describe how to use the R package fdANOVA. This package is used to test equality of weekly temperatures in Seoul and Busan through univariate functional data ANOVA, and to test equality of multivariate functional data corresponding to handwritten images using multivariate function data ANOVA.

• Communications for Statistical Applications and Methods
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• v.29 no.1
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• pp.103-125
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• 2022

In this paper, we analyze the time series data of the case and death counts of COVID-19 that broke out in China in December, 2019. The study period is during the lockdown of Wuhan. We exploit functional data analysis methods to analyze the collected time series data. The analysis is divided into three parts. First, the functional principal component analysis is conducted to investigate the modes of variation. Second, we carry out the functional canonical correlation analysis to explore the relationship between confirmed and death cases. Finally, we utilize a clustering method based on the Expectation-Maximization (EM) algorithm to run the cluster analysis on the counts of confirmed cases, where the number of clusters is determined via a cross-validation approach. Besides, we compare the clustering results with some migration data available to the public.

• Communications for Statistical Applications and Methods
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• v.25 no.6
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• pp.619-631
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• 2018

Functional data analysis continues to attract interest because advances in technology across many fields have increasingly permitted measurements to be made from continuous processes on a discretized scale. Particulate matter is among the most harmful air pollutants affecting public health and the environment, and levels of PM10 (particles less than 10 micrometers in diameter) for regions of California remain among the highest in the United States. The relatively high frequency of particulate matter sampling enables us to regard the data as functional data. In this work, we investigate the dominant modes of variation of PM10 using functional data analysis methodologies. Our analysis provides insight into the underlying data structure of PM10, and it captures the size and temporal variation of this underlying data structure. In addition, our study shows that certain aspects of size and temporal variation of the underlying PM10 structure are associated with changes in large-scale climate indices that quantify variations of sea surface temperature and atmospheric circulation patterns.

• The Korean Journal of Applied Statistics
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• v.32 no.1
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• pp.149-160
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• 2019

The electricity consumption time series data of 'A' University from July 2016 to June 2017 is analyzed via nonparametric functional data clustering since the time series data can be regarded as realization of continuous functions with dependency structure. We use a Bouveyron and Jacques (Advances in Data Analysis and Classification, 5, 4, 281-300, 2011) method based on model-based functional clustering with an FEM algorithm that assumes a Gaussian distribution on functional principal components. Clusterwise analysis is provided with cluster mean functions, densities and cluster profiles.

• Communications for Statistical Applications and Methods
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• v.28 no.2
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• pp.135-150
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• 2021

We propose principal differential analysis based classification methods. Computations of squared multiple correlation function (RSQ) and principal differential analysis (PDA) scores are reviewed; in addition, we combine principal differential analysis results with the logistic regression for binary classification. In the numerical study, we compare the principal differential analysis based classification methods with functional principal component analysis based classification. Various scenarios are considered in a simulation study, and principal differential analysis based classification methods classify the functional data well. Gene expression data is considered for real data analysis. We observe that the PDA score based method also performs well.

• Communications for Statistical Applications and Methods
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• v.20 no.4
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• pp.271-281
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• 2013

This paper considers a problem of classification of variable stars based on functional data analysis. For a better understanding of galaxy structure and stellar evolution, various approaches for classification of variable stars have been studied. Several features that explain the characteristics of variable stars (such as color index, amplitude, period, and Fourier coefficients) were usually used to classify variable stars. Excluding other factors but focusing only on the curve shapes of variable stars, Deb and Singh (2009) proposed a classification procedure using multivariate principal component analysis. However, this approach is limited to accommodate some features of the light curve data that are unequally spaced in the phase domain and have some functional properties. In this paper, we propose a light curve estimation method that is suitable for functional data analysis, and provide a classification procedure for variable stars that combined the features of a light curve with existing functional data analysis methods. To evaluate its practical applicability, we apply the proposed classification procedure to the data sets of variable stars from the project STellar Astrophysics and Research on Exoplanets (STARE).

• Journal for History of Mathematics
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• v.34 no.5
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• pp.153-164
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• 2021

A functional equation is an equation which is satisfied by a function. Some elementary functional equations can be manipulated with elementary algebraic operations and functional composition only. However to solve such functional equations, somewhat critical and creative thinking ability is required, so that it is educationally worth while teaching functional equations. In this paper, we look at the origin of functional equations, and their characteristics and educational meaning and effects. We carefully suggest the use of the functional equations as a material for school mathematics education.

• The Transactions of the Korea Information Processing Society
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• v.7 no.3
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• pp.977-991
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• 2000

In this paper, a medical image processing system was designed and implemented for morphometric and functional analysis of a human brain. The system is composed of image registration, ROI(region of interest) analysis, functional analysis, image visualization, 3D medical image database management system(DBMS), and database. The software processes an anatomical and functional image as input data, and provides visual and quantitative results. Input data and intermediate or final output data are stored to the database as several data types by the DBMS for other further image processing. In the experiment, the ROI analysis, for a normal, a tumor, a Parkinson's decease, and a depression case, showed that the system is useful for morphometric and functional analysis of a human brain.