Functional Data Analysis
TLDR
In this article, the authors provide an overview of FDA, starting with simple statistical notions such as mean and covariance functions, then covering some core techniques, the most popular of which is functional principal component analysis (FPCA).Abstract:
With the advance of modern technology, more and more data are being recorded continuously during a time interval or intermittently at several discrete time points. These are both examples of functional data, which has become a commonly encountered type of data. Functional data analysis (FDA) encompasses the statistical methodology for such data. Broadly interpreted, FDA deals with the analysis and theory of data that are in the form of functions. This paper provides an overview of FDA, starting with simple statistical notions such as mean and covariance functions, then covering some core techniques, the most popular of which is functional principal component analysis (FPCA). FPCA is an important dimension reduction tool, and in sparse data situations it can be used to impute functional data that are sparsely observed. Other dimension reduction approaches are also discussed. In addition, we review another core technique, functional linear regression, as well as clustering and classification of functional d...read more
Citations
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Density-on-Density Regression
TL;DR: In this paper , a density-on-density regression model is introduced, where the association between densities is elucidated via a warping function, and an optimization algorithm is introduced by estimating the smooth monotone transformation of the warping functions.
Journal ArticleDOI
Empirical likelihood‐based inference for functional means with application to wearable device data
Hsin‐wen Chang,Ian W. McKeague +1 more
TL;DR: In this article , a nonparametric inference framework was developed for wearable device data to construct confidence bands and compare functional means. But, their approach does not consider discontinuities in the functional covariances while accommodating discretization of the observed trajectories.
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Selection of shape-preserving, discriminative bands using supervised functional principal component analysis
TL;DR: In this article , a band selection technique based on FDA and functional PCA is proposed, which selects shape-preserving, discriminative bands which can highlight the important characteristics, variations and patterns of the hyperspectral data such that the differences between data from different classes become more apparent.
A tensor based varying-coefficient model for multi-modal neuroimaging data analysis
TL;DR: In this paper , a tensor regression model was proposed for the study of neural correlates in the presence of tensor-valued brain images and tensorvalued predictors, where both data types are collected over the same set of time points.
Posted Content
Deep Learning for Functional Data Analysis with Adaptive Basis Layers
TL;DR: In this article, the hidden units are each basis functions themselves implemented as a micro neural network, which learns to apply parsimonious dimension reduction to functional inputs that focuses only on information relevant to the target rather than irrelevant variation in the input function.
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