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We establish convergence results for a spatial semidiscretization of Mean Curvature Flow (MCF) for surfaces with fixed boundaries. Our analysis is based on Huisken's evolution equations for the mean curvature and the normal vector, enabling…
In this manuscript a unified framework for conducting inference on complex aggregated data in high dimensional settings is proposed. The data are assumed to be a collection of multiple non-Gaussian realizations with underlying undirected…
Multivariate spatial field data are increasingly common and whose modeling typically relies on building cross-covariance functions to describe cross-process relationships. An alternative viewpoint is to model the matrix of spectral…
This paper introduces a generative model for 3D surfaces based on a representation of shapes with mean curvature and metric, which are invariant under rigid transformation. Hence, compared with existing 3D machine learning frameworks, our…
Current point cloud processing algorithms do not have the capability to automatically extract semantic information from the observed scenes, except in very specialized cases. Furthermore, existing mesh analysis paradigms cannot be directly…
Modeling data using manifold values is a powerful concept with numerous advantages, particularly in addressing nonlinear phenomena. This approach captures the intrinsic geometric structure of the data, leading to more accurate descriptors…
In the continuum, close connections exist between mean curvature flow, the Allen-Cahn (AC) partial differential equation, and the Merriman-Bence-Osher (MBO) threshold dynamics scheme. Graph analogues of these processes have recently seen a…
Advancements in modern science have led to an increased prevalence of functional data, which are usually viewed as elements of the space of square-integrable functions $L^2$. Core methods in functional data analysis, such as functional…
Various 3D semantic attributes such as segmentation masks, geometric features, keypoints, and materials can be encoded as per-point probe functions on 3D geometries. Given a collection of related 3D shapes, we consider how to jointly…
Structural equation modeling (SEM) is a popular tool in the social and behavioural sciences, where it is being applied to ever more complex data types. The high-dimensional data produced by modern sensors, brain images, or (epi)genetic…
Estimation of mean and covariance functions is fundamental for functional data analysis. While this topic has been studied extensively in the literature, a key assumption is that there are enough data in the domain of interest to estimate…
Recent technological developments have enabled us to collect complex and high-dimensional data in many scientific fields, such as population health, meteorology, econometrics, geology, and psychology. It is common to encounter such datasets…
Functional data analysis in a mixed-effects model framework is done using operator calculus. In this approach the functional parameters are treated as serially correlated effects giving an alternative to the penalized likelihood approach,…
Teacher-student models provide a framework in which the typical-case performance of high-dimensional supervised learning can be described in closed form. The assumptions of Gaussian i.i.d. input data underlying the canonical teacher-student…
Dealing with massive data is a challenging task for machine learning. An important aspect of machine learning is function approximation. In the context of massive data, some of the commonly used tools for this purpose are sparsity,…
We consider the prediction problem of a continuous-time stochastic process on an entire time-interval in terms of its recent past. The approach we adopt is based on functional kernel nonparametric regression estimation techniques where…
Unlike many other works, where authors are usually focused on one or two quality criteria, the current manuscript, which is a generalization of the article [35] published in Russian, offers a multi-criteria approach to the assessment of the…
Multi-sensor data that track system operating behaviors are widely available nowadays from various engineering systems. Measurements from each sensor over time form a curve and can be viewed as functional data. Clustering of these…
Nonparametric mean function regression with repeated measurements serves as a cornerstone for many statistical branches, such as longitudinal/panel/functional data analysis. In this work, we investigate this problem using fully connected…
One of the data structures generated by medical imaging technology is high resolution point clouds representing anatomical surfaces. Raw images are in the form of triangulated surfaces and the first step is to create a standardised…