Related papers: Functional Data Analysis: An Introduction and Rece…
Structural Health Monitoring (SHM) is increasingly used in civil engineering. One of its main purposes is to detect and assess changes in infrastructure conditions to reduce possible maintenance downtime and increase safety. Ideally, this…
Multivariate functional data from a complex system are naturally high-dimensional and have complex cross-correlation structure. The complexity of data structure can be observed as that (1) some functions are strongly correlated with similar…
Multi-dimensional functional data arises in numerous modern scientific experimental and observational studies. In this paper we focus on longitudinal functional data, a structured form of multidimensional functional data. Operating within a…
High-dimensional data are crucial in biomedical research. Integrating such data from multiple studies is a critical process that relies on the choice of advanced statistical models, enhancing statistical power, reproducibility, and…
The Function point analysis (FPA) method is the preferred scheme of estimation for project managers to determine the size, effort, schedule, resource loading and other such parameters. The FPA method by International Function Point Users…
Statistical depth is the act of gauging how representative a point is compared to a reference probability measure. The depth allows introducing rankings and orderings to data living in multivariate, or function spaces. Though widely applied…
The utilization of statistical methods an their applications within the new field of study known as Topological Data Analysis has has tremendous potential for broadening our exploration and understanding of complex, high-dimensional data…
Multidimensional functional data streams arise in diverse scientific fields, yet their analysis poses significant challenges. We propose a novel online framework for functional principal component analysis that enables efficient and…
In functional data analysis (FDA), covariance function is fundamental not only as a critical quantity for understanding elementary aspects of functional data but also as an indispensable ingredient for many advanced FDA methods. This paper…
Federated analytics (FA) is a privacy-preserving framework for computing data analytics over multiple remote parties (e.g., mobile devices) or silo-ed institutional entities (e.g., hospitals, banks) without sharing the data among parties.…
Constructing generative models for functional observations is an important task in statistical functional analysis. In general, functional data contains both phase (or x or horizontal) and amplitude (or y or vertical) variability. Tradi-…
In recent years, manifold methods have moved into focus as tools for dimension reduction. Assuming that the high-dimensional data actually lie on or close to a low-dimensional nonlinear manifold, these methods have shown convincing results…
Object oriented data analysis is the statistical analysis of populations of complex objects. In the special case of functional data analysis, these data objects are curves, where standard Euclidean approaches, such as principal component…
Functional data analysis almost always involves smoothing discrete observations into curves, because they are never observed in continuous time and rarely without error. Although smoothing parameters affect the subsequent inference,…
Many fMRI analyses examine functional connectivity, or statistical dependencies among remote brain regions. Yet popular methods for studying whole-brain functional connectivity often yield results that are difficult to interpret. Factor…
The rise in data has led to the need for dimension reduction techniques, especially in the area of non-scalar variables, including time series, natural language processing, and computer vision. In this paper, we specifically investigate…
Item factor analysis (IFA) refers to the factor models and statistical inference procedures for analyzing multivariate categorical data. IFA techniques are commonly used in social and behavioral sciences for analyzing item-level response…
Confirmatory Factor Analysis (CFA) is a particular form of factor analysis, most commonly used in social research. In confirmatory factor analysis, the researcher first develops a hypothesis about what factors they believe are underlying…
Regularized discriminant analysis (RDA), proposed by Friedman (1989), is a widely popular classifier that lacks interpretability and is impractical for high-dimensional data sets. Here, we present an interpretable and computationally…
Laboratory scientists are well equipped with statistical tools for univariate data, yet many phenomena of scientific interest are time-variant or otherwise multidimensional. Functional data analysis is one way of approaching such data: by…