Related papers: Functional Data Analysis of Amplitude and Phase Va…
In many image analysis problems, the contours of objects carry important statistical information about shape. Such contours are typically affected by deformation variables including scaling, translation, rotation, and reparametrization.…
A characteristic feature of functional data is the presence of phase variability in addition to amplitude variability. Existing functional regression methods do not handle time variability in an explicit and efficient way. In this paper we…
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…
Functional data analysis, which handles data arising from curves, surfaces, volumes, manifolds and beyond in a variety of scientific fields, is a rapidly developing area in modern statistics and data science in the recent decades. The…
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…
Samples of curves, or functional data, usually present phase variability in addition to amplitude variability. Existing functional regression methods do not handle phase variability in an efficient way. In this paper we propose a functional…
This paper explores the application of functional data analysis (FDA) as a means to study the dynamics of software evolution in the open source context. Several challenges in analyzing the data from software projects are discussed, an…
We present a new method based on Functional Data Analysis (FDA) for detecting associations between one or more scalar covariates and a longitudinal response, while correcting for other variables. Our methods exploit the temporal structure…
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…
Although there are many methods for functional data analysis (FDA), little emphasis is put on characterizing variability among volatilities of individual functions. In particular, certain individuals exhibit erratic swings in their…
We develop theory and methodology for the problem of nonparametric registration of functional data that have been subjected to random deformation (warping) of their time scale. The separation of this phase variation ("horizontal" variation)…
We develop a method for constructing tolerance bounds for functional data with random warping variability. In particular, we define a generative, probabilistic model for the amplitude and phase components of such observations, which…
Functional data analyses typically proceed by smoothing, followed by functional PCA. This paradigm implicitly assumes that rough variation is due to nuisance noise. Nevertheless, relevant functional features such as time-localised or short…
The data revolution has led to an increased interest in the practice of data analysis. For a given problem, there can be significant or subtle differences in how a data analyst constructs or creates a data analysis, including differences in…
Despite of various similar features, Functional Data Analysis and High-Dimensional Data Analysis are two major fields in Statistics that grew up recently almost independently one from each other. The aim of this paper is to propose a survey…
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…
Functional data are ubiquitous in scientific modeling. For instance, quantities of interest are modeled as functions of time, space, energy, density, etc. Uncertainty quantification methods for computer models with functional response have…
Many conventional statistical and machine learning methods face challenges when applied directly to high dimensional temporal observations. In recent decades, Functional Data Analysis (FDA) has gained widespread popularity as a framework…
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 data analysis (FDA) methods have computational and theoretical appeals for some high dimensional data, but lack the scalability to modern large sample datasets. To tackle the challenge, we develop randomized algorithms for two…