• 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.

• 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.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.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.

• Communications for Statistical Applications and Methods
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• v.31 no.5
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• pp.601-612
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• 2024

A functional clustering analysis is a crucial machine learning technique in functional data analysis. Many functional clustering methods have been developed to enhance clustering performance. Moreover, due to the phase variability between functions, elastic functional clustering methods, such as applying the Fisher-Rao metric, which can manage phase variation during clustering, have been developed to improve model performance. However, aligning functions without considering the phase variation can distort functional information because phase variation can be a natural characteristic of functions. Hence, we propose a state-of-the-art functional hierarchical clustering that can manage phase and amplitude variations of functional data. This approach is based on the phase and amplitude separation method using the norm-preserving time warping of functions. Due to its invariance property, this representation provides robust variability for phase and amplitude components of functions and improves clustering performance compared to conventional functional hierarchical clustering models. We demonstrate this framework using simulated and real data.

• 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).

• 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.

• 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.

• Journal of Information Processing Systems
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• v.3 no.1
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• pp.38-42
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• 2007

Microarray data includes tens of thousands of gene expressions simultaneously, so it can be effectively used in identifying the phenotypes of diseases. However, the retrieval of functional information from a large corpus of gene expression data is still a time-consuming task. In this paper, we propose an efficient method for identifying functional categories of differentially expressed genes from a micro-array experiment by using Gene Ontology (GO). Our method is as follows: (1) The expression data set is first filtered to include only genes with mean expression values that differ by at least 3-fold between the two groups. (2) The genes are then ranked based on the t-statistics. The 100 most highly ranked genes are selected as informative genes. (3) The t-value of each informative gene is imposed as a score on the associated GO terms. High-scoring GO terms are then listed with their associated genes and represent the functional category information of the micro-array experiment. A system called HMDA (Hallym Micro-array Data analysis) is implemented on publicly available micro-array data sets and validated. Our results were also compared with the original analysis.

• Journal of Korean Society of Transportation
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• v.6 no.2
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• pp.35-48
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• 1988

Amongst various analytic methods of internal structure of city, the factor analysis method which uses O-D matrix data has some merits and characteristics compared to other methods. 1) It is possible to find one certain interaction and flow pattern between traffic zones with in a city through reanalyzing O-D data which is too complex to grasp specific meaning or pattern of flow systems. 2) It can be easily visualized the traffic flow pattern by using adequate graphic techniques, and also can clarify the functional areas whose interaction linkages are significantly strong enough between each other. In this study, the taxi traffic O-D data between 42 traffic zones in Kwang-ju city was reanalyzied by varimax rotated factor analysis methods. As a result, four factors that have significant level factor loading (over 0.5 ) and factor score (over 1.0) were sorted out. so to speak four different functional areas were clarified in Kwang-ju city, of the West, the East, the south, and the North functional areas whose interaction linkages are significantly strong enough between each other. In the study, the taxi traffic O-D data between 42 traffic zones in Kwang-ju city was reanalyzied by varimax rotated factor analysis methods. As a result, four factors that have significant level factor loading (over 0.5) and factor score 9over 1.0) were sorted out. so to speak four different functional areas were clarified in Kwang-ju city, of the West, the East, the South, and the North functional area, then these four functional areas are almost coincided with citizen's general conception of community division and administrative district. Accordingly the factor analysis methods using traffic data seems to proved to be very accurate and useful analytic instruments for analyzing flow pattern and clarifying functional areas of city, and believed to provide basic informations and criteria for practical urban land use planning and transportation planning.