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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Simultaneous Inference for Time Series Functional Linear Regression
TL;DR: In this paper , the authors considered the problem of joint simultaneous confidence band (JSCB) construction for regression coefficient functions of time series scalar-on-function linear regression when the regression model is estimated by roughness penalization approach with flexible choices of orthonormal basis functions.
On the use of the Gram matrix for multivariate functional principal components analysis
TL;DR: Using the duality of the space of observations and functional features, this article proposed to use the inner-product between the curves to estimate the eigenelements of multivariate and multidimensional functional datasets.
Journal ArticleDOI
Multiclass classification for multidimensional functional data through deep neural networks
Shuoyang Wang,Guanqun Cao +1 more
TL;DR: In this paper , a multiclass functional deep neural network (mfDNN) classifier was proposed for data mining and classification using sparse deep neural networks with rectifier linear unit (ReLU) activation function.
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Similarity-based Prognostics for Remaining Useful Life Prediction of Engineered Systems
TL;DR: In this paper , a similarity-based prognostic approach for accurate RUL prediction is presented, where historical degradation trajectories are properly abstracted into the common degrading characteristics (i.e., one mean trend and a few varying modes) for the whole system population by functional principal component analysis, so that the capacity of degradation trajectory library is greatly reduced.
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Ambulatory assessment to predict problem anger in trauma-affected adults: Study protocol
Olivia Metcalf,Laura Finlayson-Short,Karen E. Lamb,Sophie Zaloumis,Meaghan O'Donnell,Tianchen Qian,Tracey Varker,Sean Cowlishaw,Melissa A. Brotman,David Forbes +9 more
TL;DR: In this paper , the authors evaluated the feasibility and acceptability of ambulatory assessment in a trauma-affected population, and determined whether a continuously measured physiological indicator of stress predicts self-reported anger intensity.
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