Discrete functional data analysis

Mizuta, Masahiro

doi:10.1007/978-3-7908-1709-6_28

Cited by 4 publications

(2 citation statements)

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“…Recently, functional data analysis has received considerable attention in different fields of application such as criminology, electromyography, signal processing, and a number of successful applications have been reported (see, e.g., Silverman 2002, 2005;Araki and Konishi 2006;Mizuta 2006).…”

Section: Introductionmentioning

confidence: 98%

Functional regression modeling via regularized Gaussian basis expansions

et al. 2008

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Section: Introductionmentioning

confidence: 98%

Functional regression modeling via regularized Gaussian basis expansions

et al. 2008

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“…These functional approaches are referred to as functional data analysis (FDA; Silverman (2002, 2005), Ferraty and Vieu (2006), Mizuta (2006)). The basic idea behind FDA is the conversion of observational discrete data to functional data by a smoothing method and then extracting information from the obtained functional data set by applying concepts from traditional multivariate analysis.…”

Section: Introductionmentioning

confidence: 99%

Functional principal component analysis via regularized Gaussian basis expansions and its application to unbalanced data

Kayano

Konishi

2009

Journal of Statistical Planning and Inference

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This paper introduces regularized functional principal component analysis for multidimensional functional data sets, utilizing Gaussian basis functions. An essential point in a functional approach via basis expansions is the evaluation of the matrix for the integral of the product of any two bases (cross product matrix). Advantages of the use of the Gaussian type of basis functions in the functional approach are that its cross product matrix can be easily calculated, and it creates a much more flexible instrument for transforming each individual's observation into a functional form. The proposed method is applied to the analysis of three-dimensional (3D) protein structural data that can be referred to as unbalanced data. It is shown that our method extracts useful information from unbalanced data. Numerical experiments are conducted to investigate the effectiveness of our method via Gaussian basis functions, comparing to the method based on B-splines. On performing regularized functional principal component analysis with B-splines, we also derive the exact form of its cross product matrix. The numerical results show that our methodology is superior to that based on B-splines for unbalanced data.

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Functional Data Analysis and Its Application

Mizuta

Kato

Rough Sets and Knowledge Technology

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Discrete functional data analysis

Cited by 4 publications

References 4 publications

Functional regression modeling via regularized Gaussian basis expansions

Functional regression modeling via regularized Gaussian basis expansions

Functional principal component analysis via regularized Gaussian basis expansions and its application to unbalanced data

Functional Data Analysis and Its Application

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