Related papers: Spatially Penalised Registration of Multivariate F…
Predicting missing segments in partially observed functions is challenging due to infinite-dimensionality, complex dependence within and across observations, and irregular noise. These challenges are further exacerbated by the existence of…
Multivariate functional data are becoming ubiquitous with advances in modern technology and are substantially more complex than univariate functional data. We propose and study a novel model for multivariate functional data where the…
The function-on-function regression model is fundamental for analyzing relationships between functional covariates and responses. However, most existing function-on-function regression methodologies assume independence between observations,…
Inspired by several recent developments in regularization theory, optimization, and signal processing, we present and analyze a numerical approach to multi-penalty regularization in spaces of sparsely represented functions. The sparsity…
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)…
One of the challenges with functional data is incorporating spatial structure, or local correlation, into the analysis. This structure is inherent in the output from an increasing number of biomedical technologies, and a functional linear…
Spatiotemporal matrix-valued data arise frequently in modern applications, yet performing effective regression analysis remains challenging due to complex, dimension-specific dependencies. In this work, we propose a regularized framework…
Spatial, amplitude and phase variations in spatial functional data are confounded. Conclusions from the popular functional trace variogram, which quantifies spatial variation, can be misleading when analysing misaligned functional data with…
Functional data registration is a critical challenge in modern statistics, essential for separating phase variability from amplitude variability. While derivative-based frameworks offer mathematically elegant solutions, their dependence on…
In the realm of large-scale spatiotemporal data, abrupt changes are commonly occurring across both spatial and temporal domains. This study aims to address the concurrent challenges of detecting change points and identifying spatial…
Multivariate functional data present theoretical and practical complications which are not found in univariate functional data. One of these is a situation where the component functions of multivariate functional data are positive and are…
We extend the definition of functional data registration to encompass a larger class of registered functions. In contrast to traditional registration models, we allow for registered functions that have more than one primary direction of…
This work studies the multi-task functional linear regression models where both the covariates and the unknown regression coefficients (called slope functions) are curves. For slope function estimation, we employ penalized splines to…
Achieving high-performance in multi-object tracking algorithms heavily relies on modeling spatio-temporal relationships during the data association stage. Mainstream approaches encompass rule-based and deep learning-based methods for…
Ordinal data occur frequently in the social sciences. When applying principal component analysis (PCA), however, those data are often treated as numeric implying linear relationships between the variables at hand, or non-linear PCA is…
This paper gives a comprehensive treatment of the convergence rates of penalized spline estimators for simultaneously estimating several leading principal component functions, when the functional data is sparsely observed. The penalized…
For multivariate nonparametric regression, functional analysis-of-variance (ANOVA) modeling aims to capture the relationship between a response and covariates by decomposing the unknown function into various components, representing main…
We propose a coercive approach to simultaneously register and segment multi-modal images which share similar spatial structure. Registration is done at the region level to facilitate data fusion while avoiding the need for interpolation.…
Multivariate functional data can be intrinsically multivariate like movement trajectories in 2D or complementary like precipitation, temperature, and wind speeds over time at a given weather station. We propose a multivariate functional…
Large volumes of spatiotemporal data, characterized by high spatial and temporal variability, may experience structural changes over time. Unlike traditional change-point problems, each sequence in this context consists of function-valued…