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Functional principal component analysis (FPCA) is a fundamental tool and has attracted increasing attention in recent decades, while existing methods are restricted to data with a single or finite number of random functions (much smaller…
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…
Functional principal component analysis (FPCA) has been widely used to capture major modes of variation and reduce dimensions in functional data analysis. However, standard FPCA based on the sample covariance estimator does not work well in…
This paper introduces a robust estimation strategy for the spatial functional linear regression model using dimension reduction methods, specifically functional principal component analysis (FPCA) and functional partial least squares…
Functional Principal Component Analysis (FPCA) has become a widely-used dimension reduction tool for functional data analysis. When additional covariates are available, existing FPCA models integrate them either in the mean function or in…
Functional principal component analysis (FPCA) is a widely used technique in functional data analysis for identifying the primary sources of variation in a sample of random curves. The eigenfunctions obtained from standard FPCA typically…
Functional principal component analysis (FPCA) is a key tool in the study of functional data, driving both exploratory analyses and feature construction for use in formal modeling and testing procedures. However, existing methods for FPCA…
Functional principal component analysis (FPCA) is an important technique for dimension reduction in functional data analysis (FDA). Classical FPCA method is based on the Karhunen-Lo\`{e}ve expansion, which assumes a linear structure of the…
Functional data analysis is an important research field in statistics which treats data as random functions drawn from some infinite-dimensional functional space, and functional principal component analysis (FPCA) based on…
In recent times, functional data analysis (FDA) has been successfully applied in the field of high dimensional data classification. In this paper, we present a novel classification framework using functional data and classwise Principal…
Dimension reduction is crucial in functional data analysis (FDA). The key tool to reduce the dimension of the data is functional principal component analysis. Existing approaches for functional principal component analysis usually involve…
Functional principal components (FPC's) provide the most important and most extensively used tool for dimension reduction and inference for functional data. The selection of the number, d, of the FPC's to be used in a specific procedure has…
For very large datasets, random projections (RP) have become the tool of choice for dimensionality reduction. This is due to the computational complexity of principal component analysis. However, the recent development of randomized…
Sparse principal component analysis (PCA) aims at mapping large dimensional data to a linear subspace of lower dimension. By imposing loading vectors to be sparse, it performs the double duty of dimension reduction and variable selection.…
Traditional principal component analysis (PCA) is well known in high-dimensional data analysis, but it requires to express data by a matrix with observations to be continuous. To overcome the limitations, a new method called flexible PCA…
The literature on high-dimensional functional data focuses on either the dependence over time or the correlation among functional variables. In this paper, we propose a factor-guided functional principal component analysis (FaFPCA) method…
We study semiparametric factor models in high-dimensional panels where the factor loadings consist of a nonparametric component explained by observed covariates and an idiosyncratic component capturing unobserved heterogeneity. A key…
Functional data analysis is concerned with the analysis of infinite-dimensional data functions. Functional principal component analysis (FPCA) is a key method to obtain finite-dimensional summaries. Consistency of FPCA has been…
In this paper we review existing methods for robust functional principal component analysis (FPCA) and propose a new method for FPCA that can be applied to longitudinal data where only a few observations per trajectory are available. This…
Massive data bring the big challenges of memory and computation for analysis. These challenges can be tackled by taking subsamples from the full data as a surrogate. For functional data, it is common to collect multiple measurements over…