• Title, Summary, Keyword: functional data analysis

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Functional Data Analysis of Temperature and Precipitation Data (기온 강수량 자료의 함수적 데이터 분석)

  • Kang, Kee-Hoon;Ahn, Hong-Se
    • 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.

Functional Data Classification of Variable Stars

  • Park, Minjeong;Kim, Donghoh;Cho, Sinsup;Oh, Hee-Seok
    • 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).

Investigating the underlying structure of particulate matter concentrations: a functional exploratory data analysis study using California monitoring data

  • Montoya, Eduardo L.
    • 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.

Nonparametric clustering of functional time series electricity consumption data (전기 사용량 시계열 함수 데이터에 대한 비모수적 군집화)

  • Kim, Jaehee
    • 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.

Medical Image Processing System for Morphometric and Functional Analysis of a Human Brain (인간 뇌의 형태적 및 기능적 분석을 위한 의료영상 처리시스템)

  • Kim, Tae-U
    • 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.

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An Efficient Functional Analysis Method for Micro-array Data Using Gene Ontology

  • Hong, Dong-Wan;Lee, Jong-Keun;Park, Sung-Soo;Hong, Sang-Kyoon;Yoon, Jee-Hee
    • 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.

Functional Areas of Kwang-ju City through Analysis of the Taxi-flow Pattern (택시통행패턴에 따른 광주시 기능지역 분석)

  • 김영기
    • 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.

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Principal component analysis for Hilbertian functional data

  • Kim, Dongwoo;Lee, Young Kyung;Park, Byeong U.
    • Communications for Statistical Applications and Methods
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    • v.27 no.1
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    • pp.149-161
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    • 2020
  • In this paper we extend the functional principal component analysis for real-valued random functions to the case of Hilbert-space-valued functional random objects. For this, we introduce an autocovariance operator acting on the space of real-valued functions. We establish an eigendecomposition of the autocovariance operator and a Karuhnen-Loève expansion. We propose the estimators of the eigenfunctions and the functional principal component scores, and investigate the rates of convergence of the estimators to their targets. We detail the implementation of the methodology for the cases of compositional vectors and density functions, and illustrate the method by analyzing time-varying population composition data. We also discuss an extension of the methodology to multivariate cases and develop the corresponding theory.

A Study on the Requirements Allocation and Tracking by Implementing Functional Analysis (기능분석을 이용한 항공기 설계요구의 할당 및 추적에 관한 연구)

  • 이재우
    • Journal of the Korea Institute of Military Science and Technology
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    • v.2 no.2
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    • pp.52-60
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    • 1999
  • By implementing the Systems Engineering process for the aircraft preliminary design, functional analysis study is performed, hence Functional Interface Data Flow(FIDF) and Functional Flow Block Diagram(FFBD) are generated. Based on FIDF and FFBD, allocable and non-allocable design/performance/RM&S requirements are allocated to the appropriate levels. Weight and cost tracking and design margin management methodologies are studied and implemented for the balanced aircraft design.

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Classical testing based on B-splines in functional linear models (함수형 선형모형에서의 B-스플라인에 기초한 검정)

  • Sohn, Jihoon;Lee, Eun Ryung
    • The Korean Journal of Applied Statistics
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    • v.32 no.4
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    • pp.607-618
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    • 2019
  • A new and interesting task in statistics is to effectively analyze functional data that frequently comes from advances in modern science and technology in areas such as meteorology and biomedical sciences. Functional linear regression with scalar response is a popular functional data analysis technique and it is often a common problem to determine a functional association if a functional predictor variable affects the scalar response in the models. Recently, Kong et al. (Journal of Nonparametric Statistics, 28, 813-838, 2016) established classical testing methods for this based on functional principal component analysis (of the functional predictor), that is, the resulting eigenfunctions (as a basis). However, the eigenbasis functions are not generally suitable for regression purpose because they are only concerned with the variability of the functional predictor, not the functional association of interest in testing problems. Additionally, eigenfunctions are to be estimated from data so that estimation errors might be involved in the performance of testing procedures. To circumvent these issues, we propose a testing method based on fixed basis such as B-splines and show that it works well via simulations. It is also illustrated via simulated and real data examples that the proposed testing method provides more effective and intuitive results due to the localization properties of B-splines.