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Contrastive Functional Principal Components Analysis. [PDF]
Proc AAAI Conf Artif IntellAs functional data assumes a central role in contemporary data analysis, the search for meaningful dimension reduction becomes critical due to its inherent infinite-dimensional structure. Traditional methods, such as Functional Principal Component Analysis (FPCA), adeptly explore the overarching structures within the functional data.
Zhang E, Li D.
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Functional principal components analysis of workload capacity functions. [PDF]
Behav Res Methods, 2013 Workload capacity, an important concept in many areas of psychology, describes processing efficiency across changes in workload. The capacity coefficient is a function across time that provides a useful measure of this construct. Until now, most analyses of the capacity coefficient have focused on the magnitude of this function, and often only in terms
Burns DM +3 more
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Longitudinal functional principal component analysis [PDF]
Electronic Journal of Statistics, 2010 We introduce models for the analysis of functional data observed at multiple time points. The dynamic behavior of functional data is decomposed into a time-dependent population average, baseline (or static) subject-specific variability, longitudinal (or dynamic) subject-specific variability, subject-visit-specific variability and measurement error. The
Greven, Sonja +3 more
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Structured Functional Principal Component Analysis [PDF]
Biometrics, 2014 Summary Motivated by modern observational studies, we introduce a class of functional models that expand nested and crossed designs. These models account for the natural inheritance of the correlation structures from sampling designs in studies where the fundamental unit is a function or image. Inference is based on functional quadratics
Shou, Haochang +3 more
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Sparse and Functional Principal Components Analysis [PDF]
2019 IEEE Data Science Workshop (DSW), 2019 The published version of this paper incorrectly thanks "Luofeng Luo" instead of "Luofeng Liao" in the ...
Genevera I. Allen, Michael Weylandt
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On Properties of Functional Principal Components Analysis [PDF]
Journal of the Royal Statistical Society Series B: Statistical Methodology, 2005 SummaryFunctional data analysis is intrinsically infinite dimensional; functional principal component analysis reduces dimension to a finite level, and points to the most significant components of the data. However, although this technique is often discussed, its properties are not as well understood as they might be.
Hall, Peter, Hosseini-Nasab, Seyed
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Localized Functional Principal Component Analysis [PDF]
Journal of the American Statistical Association, 2015 We propose localized functional principal component analysis (LFPCA), looking for orthogonal basis functions with localized support regions that explain most of the variability of a random process. The LFPCA is formulated as a convex optimization problem through a novel deflated Fantope localization method and is implemented through an efficient ...
Chen, Kehui, Lei, Jing
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Interpretable Functional Principal Component Analysis
Biometrics, 2015 SummaryFunctional principal component analysis (FPCA) is a popular approach to explore major sources of variation in a sample of random curves. These major sources of variation are represented by functional principal components (FPCs). The intervals where the values of FPCs are significant are interpreted as where sample curves have major variations ...
Lin, Zhenhua +2 more
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Multi-dimensional functional principal component analysis [PDF]
Statistics and Computing, 2016 Functional principal component analysis is one of the most commonly employed approaches in functional and longitudinal data analysis and we extend it to analyze functional/longitudinal data observed on a general $d$-dimensional domain. The computational issues emerging in the extension are fully addressed with our proposed solutions.
Lu-Hung Chen, Ci-Ren Jiang
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Eigen-Adjusted Functional Principal Component Analysis
Journal of Computational and Graphical Statistics, 2022 Functional Principal Component Analysis (FPCA) has become a widely-used dimension reduction tool for functional data analysis. When additional covariates are available, existing FPCA models integrate them either in the mean function or in both the mean function and the covariance function.
Ci-Ren Jiang +3 more
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