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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Journal ArticleDOI
Incorporating covariate into mean and covariance function estimation of functional data under a general weighing scheme
TL;DR: In this paper , the authors developed the estimation method of mean and covariance functions of functional data with additional covariate information and established the uniform convergence rates of the estimators in the general weighing scheme.
Journal ArticleDOI
Application of distance standard deviation in functional data analysis
Mirosław Krzyśko,Łukasz Smaga +1 more
TL;DR: In this article , the authors apply the distance standard deviation constructed based on distance correlation, which was recently introduced as a measure of spread, to measure the variability of functional data, not only scale differences.
Proceedings ArticleDOI
Multivariate Time Series Analysis: An Interpretable CNN-based Model
TL;DR: In this paper , the authors propose a new approach to interpret the CNN outputs by extracting and clustering the activated time series sequences learned from a trained network, and visualize the data representative features.
A Karhunen-Lo\`{e}ve Theorem for Random Flows in Hilbert spaces
TL;DR: In this paper , a generalisation of Mercer's theorem to operator-valued kernels in infinite dimensional Hilbert spaces is presented, and a series expansion with uncorrelated coefficients for square-integrable random flows in a Hilbert space, that holds uniformly over time.
Posted Content
Mean curvature and mean shape for multivariate functional data under Frenet-Serret framework.
Juhyun Park,Nicolas J.-B. Brunel +1 more
TL;DR: A new framework for functional data as multidimensional curves that allows us to extract geometrical features from noisy data and defines a mean through measuring shape variation of the curves through the Frenet-Serret ordinary differential equation.
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