Related papers: Review of Functional Data Analysis
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 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…
As high-dimensional and high-frequency data are being collected on a large scale, the development of new statistical models is being pushed forward. Functional data analysis provides the required statistical methods to deal with large-scale…
Multivariate functional principal component analysis (MFPCA) is a powerful dimension reduction technique for analyzing multiple functional variables simultaneously. However, existing MFPCA methods assume that all functional observations are…
When measurements fall below or above a detection threshold, the resulting data are missing not at random (MNAR), posing challenges for statistical analysis. For example, in longitudinal biomarker studies, observations may be subject to…
Big data is transforming our world, revolutionizing operations and analytics everywhere, from financial engineering to biomedical sciences. The complexity of big data often makes dimension reduction techniques necessary before conducting…
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…
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…
Functional data analysis (FDA) is a part of modern multivariate statistics that analyses data providing information about curves, surfaces or anything else varying over a certain continuum. In economics and empirical finance we often have…
Many scientific areas are faced with the challenge of extracting information from large, complex, and highly structured data sets. A great deal of modern statistical work focuses on developing tools for handling such data. This paper…
The abundance of functional observations in scientific endeavors has led to a significant development in tools for functional data analysis (FDA). This kind of data comes with several challenges: infinite-dimensionality of function spaces,…
Functional Principal Components Analysis (FPCA) provides a parsimonious, semi-parametric model for multivariate, sparsely-observed functional data. Frequentist FPCA approaches estimate principal components (PCs) from the data, then…
Functional time series (FTS) data have become increasingly available in real-world applications. Research on such data typically focuses on two objectives: curve reconstruction and forecasting, both of which require efficient dimension…
As edge devices become increasingly powerful, data analytics are gradually moving from a centralized to a decentralized regime where edge compute resources are exploited to process more of the data locally. This regime of analytics is…
In functional data analysis, replicate observations of a smooth functional process and its derivatives offer a unique opportunity to flexibly estimate continuous-time ordinary differential equation models. Ramsay (1996) first proposed to…
Multilinear Principal Component Analysis (MPCA) is a widely utilized method for the dimension reduction of tensor data. However, the integration of MPCA into federated learning remains unexplored in existing research. To tackle this gap,…
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…
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…
When functional data manifest amplitude and phase variations, a commonly-employed framework for analyzing them is to take away the phase variation through a function alignment and then to apply standard tools to the aligned functions. A…
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…