Related papers: Functional Singular Spectrum Analysis
Functional principal component analysis is one of the most commonly employed approaches in functional and longitudinal data analysis and we extend it to analyze functional/longitudinal data observed on a general $d$-dimensional domain. The…
Sparse principal component analysis (SPCA) has emerged as a powerful technique for modern data analysis, providing improved interpretation of low-rank structures by identifying localized spatial structures in the data and disambiguating…
This paper tackles one of the most fundamental goals in functional time series analysis which is to provide reliable predictions for future functions. Existing methods for predicting a complete future functional observation use only…
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…
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 data analysis (FDA) involves the analysis of data whose ideal units of observation are functions defined on some continuous domain, and the observed data consist of a sample of functions taken from some population, sampled on a…
Classification (supervised-learning) of multivariate functional data is considered when the elements of the random functional vector of interest are defined on different domains. In this setting, PLS classification and tree PLS-based…
Simultaneous sparse approximation (SSA) seeks to represent a set of dependent signals using sparse vectors with identical supports. The SSA model has been used in various signal and image processing applications involving multiple…
We propose a novel class of prior distributions for sequences of orthogonal functions, which are frequently required in various statistical models such as functional principal component analysis (FPCA). Our approach constructs priors…
Data with multiple functional recordings at each observational unit are increasingly common in various fields including medical imaging and environmental sciences. To conduct inference for such observations, we develop a paired two-sample…
Functional linear regression analysis aims to model regression relations which include a functional predictor. The analog of the regression parameter vector or matrix in conventional multivariate or multiple-response linear regression…
Multifractal detrended fluctuation analysis (MFDFA) has become a central method to characterise the variability and uncertainty in empiric time series. Extracting the fluctuations on different temporal scales allows quantifying the strength…
The analysis of multivariate functional curves has the potential to yield important scientific discoveries in domains such as healthcare, medicine, economics and social sciences. However, it is common for real-world settings to present…
Approaches to automated grouping in singular spectrum analysis are considered. A new method for the identification of periodic components is proposed. The possibilities of extensions to multivariate time series and images are discussed.
Functional data analysis is becoming increasingly popular to study data from real-valued random functions. Nevertheless, there is a lack of multiple testing procedures for such data. These are particularly important in factorial designs to…
Our research proposes a novel method for reducing the dimensionality of functional data, specifically for the case where the response is a scalar and the predictor is a random function. Our method utilizes distance covariance, and has…
We present a Bayesian approach for modeling multivariate, dependent functional data. To account for the three dominant structural features in the data--functional, time dependent, and multivariate components--we extend hierarchical dynamic…
Modern mobile health (mHealth) assessment combines self-reported measures of participants' health experiences with passively collected health behavior data throughout the day. These data are collected across multiple measurement scales,…
This work introduces a new functional series for expanding an analytic function in terms of an arbitrary analytic function. It is generally applicable and straightforward to use. It is also suitable for approximating the behavior of a…
I introduce Forecastable Component Analysis (ForeCA), a novel dimension reduction technique for temporally dependent signals. Based on a new forecastability measure, ForeCA finds an optimal transformation to separate a multivariate time…