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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Discussion: A Spatial Modeling Approach for Linguistic Object Data: Analyzing Dialect Sound Variations Across Great Britain, by Shahin Tavakoli et al.
TL;DR: Tavakoli et al. as discussed by the authors proposed covariance objects in the context of linguistic analy... and they made a timely and interesting contribution to the emerging field of object data.
Posted ContentDOI
Functional Ensemble Survival Tree: Dynamic Prediction of Alzheimer’s Disease Progression Accommodating Multiple Time-Varying Covariates
TL;DR: The proposed framework incorporates multivariate functional principal component analysis to characterize the changing patterns of multiple time-varying neurocognitive biomarker trajectories and nest these features within an ensemble survival tree in predicting the progression of AD.
Journal ArticleDOI
Explainable multi-class anomaly detection on functional data
TL;DR: The anomaly detection procedure consists of transforming the series into a vector of features and using an Isolation forest algorithm and the explainable procedure is based on the computation of the SHAP coefficients and on the use of a supervised decision tree.
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Exploration of the impact of political ideology disparity on COVID-19 transmission in the United States
TL;DR: In this paper , the authors explored the impact of personal political ideology disparity on COVID-19 transmission before and after the emergence of Omicron and established a new index, which depended on the daily cumulative number of confirmed cases in each state and the corresponding population size.
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Functional spherical autocorrelation: A robust estimate of the autocorrelation of a functional time series
TL;DR: The spherical autocorrelation as discussed by the authors measure is based on measuring the average angle between lagged pairs of series after having been projected onto the unit sphere, which describes a notion of sign or direction of serial dependence in the series.
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