Functional principal component analysis
View article: Functional Data Analysis
Functional Data Analysis Open
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 enc…
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Multivariate Functional Principal Component Analysis for Data Observed on Different (Dimensional) Domains Open
Existing approaches for multivariate functional principal component analysis are restricted to data on the same one-dimensional interval. The presented approach focuses on multivariate functional data on different domains that may differ i…
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Functional data analysis for density functions by transformation to a Hilbert space Open
Functional data that are nonnegative and have a constrained integral can be considered as samples of one-dimensional density functions. Such data are ubiquitous. Due to the inherent constraints, densities do not live in a vector space and,…
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A systematic comparison of PCA‐based Statistical Process Monitoring methods for high‐dimensional, time‐dependent Processes Open
High‐dimensional and time‐dependent data pose significant challenges to Statistical Process Monitoring. Most of the high‐dimensional methodologies to cope with these challenges rely on some form of Principal Component Analysis (PCA) model,…
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Review of Functional Data Analysis Open
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. They are both examples of "functional data", which have become a prevailing…
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Principal component analysis for functional data on Riemannian manifolds and spheres Open
Functional data analysis on nonlinear manifolds has drawn recent interest. Sphere-valued functional data, which are encountered, for example, as movement trajectories on the surface of the earth are an important special case. We consider a…
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New Modeling Approaches Based on Varimax Rotation of Functional Principal Components Open
Functional Principal Component Analysis (FPCA) is an important dimension reduction technique to interpret the main modes of functional data variation in terms of a small set of uncorrelated variables. The principal components can not alway…
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A Multi-Dimensional Functional Principal Components Analysis of EEG Data Open
Summary The electroencephalography (EEG) data created in event-related potential (ERP) experiments have a complex high-dimensional structure. Each stimulus presentation, or trial, generates an ERP waveform which is an instance of functiona…
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Automatic Classification of Functional Gait Disorders Open
This paper proposes a comprehensive investigation of the automatic classification of functional gait disorders (GDs) based solely on ground reaction force (GRF) measurements. The aim of this study is twofold: first, to investigate the suit…
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Classical testing in functional linear models Open
We extend four tests common in classical regression – Wald, score, likelihood ratio and F tests – to functional linear regression, for testing the null hypothesis, that there is no association between a scalar response and a functional cov…
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Smooth Principal Component Analysis over two-dimensional manifolds with an application to neuroimaging Open
Motivated by the analysis of high-dimensional neuroimaging signals located over the cortical surface, we introduce a novel Principal Component Analysis technique that can handle functional data located over a two-dimensional manifold. For …
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Localized Functional Principal Component Analysis Open
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 optim…
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Testing for stationarity of functional time series in the frequency domain Open
Interest in functional time series has spiked in the recent past with papers covering both methodology and applications being published at a much increased pace. This article contributes to the research in this area by proposing a new stat…
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Functional CAR Models for Large Spatially Correlated Functional Datasets Open
We develop a functional conditional autoregressive (CAR) model for spatially correlated data for which functions are collected on areal units of a lattice. Our model performs functional response regression while accounting for spatial corr…
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Functional principal component analysis of spatially correlated data Open
This paper focuses on the analysis of spatially correlated functional data. We propose a parametric model for spatial correlation and the between-curve correlation is modeled by correlating functional principal component scores of the func…
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Fast covariance estimation for multivariate sparse functional data Open
Covariance estimation is essential yet underdeveloped for analysing multivariate functional data. We propose a fast covariance estimation method for multivariate sparse functional data using bivariate penalized splines. The tensor‐product …
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Unvealing the Principal Modes of Human Upper Limb Movements through Functional Analysis Open
The rich variety of human upper limb movements requires an extraordinary coordination of different joints according to specific spatio-temporal patterns. However, unvealing these motor schemes is a challenging task. Principal components ha…
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Phantom oscillations in principal component analysis Open
Principal component analysis (PCA) is a dimensionality reduction method that is known for being simple and easy to interpret. Principal components are often interpreted as low-dimensional patterns in high-dimensional space. However, this s…
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Predicting Brain Age Based on Spatial and Temporal Features of Human Brain Functional Networks Open
The organization of human brain networks can be measured by capturing correlated brain activity with functional MRI data. There have been a variety of studies showing that human functional connectivities undergo an age-related change over …
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Mapping Mediterranean Forest Plant Associations and Habitats with Functional Principal Component Analysis Using Landsat 8 NDVI Time Series Open
The classification of plant associations and their mapping play a key role in defining habitat biodiversity management, monitoring, and conservation strategies. In this work we present a methodological framework to map Mediterranean forest…
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Testing for periodicity in functional time series Open
We derive several tests for the presence of a periodic component in a time series of functions. We consider both the traditional setting in which the periodic functional signal is contaminated by functional white noise, and a more general …
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Recent developments in complex and spatially correlated functional data Open
As high-dimensional and high-frequency data are being collected on a large\nscale, the development of new statistical models is being pushed forward.\nFunctional data analysis provides the required statistical methods to deal with\nlarge-s…
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Hybrid principal components analysis for region-referenced longitudinal functional EEG data Open
Summary Electroencephalography (EEG) data possess a complex structure that includes regional, functional, and longitudinal dimensions. Our motivating example is a word segmentation paradigm in which typically developing (TD) children, and …
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Functional Data Analysis: An Introduction and Recent Developments Open
Functional data analysis (FDA) is a statistical framework that allows for the analysis of curves, images, or functions on higher dimensional domains. The goals of FDA, such as descriptive analyses, classification, and regression, are gener…
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Prediction of working memory ability based on EEG by functional data analysis Open
The data analytics suggest that a multiple functional linear regression model for the predictive relationship between working memory ability and frontal activity of the brain is both feasible and accurate via EEG signal processing.
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Bayesian Estimation of Principal Components for Functional Data Open
The area of principal components analysis (PCA) has seen relatively few contributions from the Bayesian school of inference. In this paper, we propose a Bayesian method for PCA in the case of functional data observed with error. We suggest…
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A novel stroke lesion network mapping approach: improved accuracy yet still low deficit prediction Open
Lesion network mapping estimates functional network abnormalities caused by a focal brain lesion. The method requires embedding the volume of the lesion into a normative functional connectome and using the average functional magnetic reson…
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Long-term forecasting oriented to urban expressway traffic situation Open
Long-term traffic forecasting has become a basic and critical work in the research on road traffic congestion. It plays an important role in alleviating road traffic congestion and improving traffic management quality. According to the pro…
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Modeling Temporal Variation in Physical Activity Using Functional Principal Components Analysis Open
Accelerometers are person-worn sensors that provide objective measurements of movement based on minute-level activity counts, thus providing a rich framework for assessing physical activity patterns. New statistical approaches and computat…
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Principal Component Analysis Reveals the Proximal to Distal Pattern in Vertical Jumping Is Governed by Two Functional Degrees of Freedom Open
The successful completion of motor tasks requires effective control of multiple degrees of freedom (DOF), with adaptations occurring as a function of varying performance constraints. In this study we sought to compare the emergent coordina…