Related papers: Functional archetype and archetypoid analysis

A new method is proposed to perform joint analysis of longitudinal and cross-sectional growth data. Clustering is first performed to group similar subjects in cross-sectional data to form a pseudo longitudinal data set, then the pseudo…

Data can be assumed to be continuous functions defined on an infinite-dimensional space for many phenomena. However, the infinite-dimensional data might be driven by a small number of latent variables. Hence, factor models are relevant for…

Functional data are frequently accompanied by a parametric template that describes the typical shapes of the functions. However, these parametric templates can incur significant bias, which undermines both utility and interpretability. To…

Functional data are typically modeled as sample paths of smooth stochastic processes in order to mitigate the fact that they are often observed discretely and noisily, occasionally irregularly and sparsely. The smoothness assumption is…

Modeling functions that are sequentially observed as functional time series is becoming increasingly common. In such models, it is often crucial to ensure data homogeneity. We investigate the sensitivity of graph-based change point…

Classical multivariate principal component analysis has been extended to functional data and termed functional principal component analysis (FPCA). Most existing FPCA approaches do not accommodate covariate information, and it is the goal…

Due to developments in instruments and computers, functional observations are increasingly popular. However, effective methodologies for flexibly estimating the underlying trends with valid uncertainty quantification for a sequence of…

Archetypal analysis (AA) was originally proposed in 1994 by Adele Cutler and Leo Breiman as a computational procedure for extracting distinct aspects, so-called archetypes, from observations, with each observational record approximated as a…

We propose an alternative to $k$-nearest neighbors for functional data whereby the approximating neighboring curves are piecewise functions built from a functional sample. Using a locally defined distance function that satisfies…

Functional data analysis is typically performed in two steps: first, functionally representing discrete observations, and then applying functional methods to the so-represented data. The initial choice of a functional representation may…

In the last few decades, building regression models for non-scalar variables, including time series, text, image, and video, has attracted increasing interests of researchers from the data analytic community. In this paper, we focus on a…

Spatial functional data arise in many settings, such as particulate matter curves observed at monitoring stations and age population curves at each areal unit. Most existing functional regression models have limited applicability because…

Algebraic characterizations of the computational aspects of functions defined over the real numbers provide very effective tool to understand what computability and complexity over the reals, and generally over continuous spaces, mean. This…

We introduce a deep multitask architecture to integrate multityped representations of multimodal objects. This multitype exposition is less abstract than the multimodal characterization, but more machine-friendly, and thus is more precise…

Many modern datasets, from areas such as neuroimaging and geostatistics, come in the form of a random sample of tensor-valued data which can be understood as noisy observations of a smooth multidimensional random function. Most of the…

Data analyses are often constructed in an imperative manner, where commands representing actions taken on the data are issued sequentially. The publication of these commands, along with the data, is essential to the reproducibility of the…

Mathematical formulations and proofs for a wavelet based statistic employed in functional data analysis is elaborately discussed in this report. The propositions and derivations discussed here apply to a wavelet based statistic with hard…

Using representations of functional data can be more convenient and beneficial in subsequent statistical models than direct observations. These representations, in a lower-dimensional space, extract and compress information from individual…

In a previous paper [1] it was discussed the viability of functional analysis using as a basis a couple of generic functions, and hence vectorial decomposition. Here we complete the paradigm exploiting one of the analysis methodologies…

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…