Related papers: Embedding Functional Data: Multidimensional Scalin…

In this paper, we introduce a new functional point of view on bilevel optimization problems for machine learning, where the inner objective is minimized over a function space. These types of problems are most often solved by using methods…

Orchestrating parametric fitting of multicomponent spectra at scale is an essential yet underappreciated task in high-throughput quantification of materials and chemical composition. To automate the annotation process for spectroscopic and…

Over the decades, Functional Analysis has been enriched and inspired on account of demands from neighboring fields, within mathematics, harmonic analysis (wavelets and signal processing), numerical analysis (finite element methods,…

Multimodal learning, a rapidly evolving field in artificial intelligence, seeks to construct more versatile and robust systems by integrating and analyzing diverse types of data, including text, images, audio, and video. Inspired by the…

An important task for many if not all the scientific domains is efficient knowledge integration, testing and codification. It is often solved with model construction in a controllable computational environment. In spite of that, the…

Data scaling has revolutionized research fields like natural language processing, computer vision, and robotics control, providing foundation models with remarkable multi-task and generalization capabilities. In this paper, we investigate…

This paper considers the problem of finding a meaningful template function that represents the common pattern of a sample of curves. To address this issue, a novel algorithm based on a robust version of the isometric featuring mapping…

A fundamental problem in manifold learning is to approximate a functional relationship in a data chosen randomly from a probability distribution supported on a low dimensional sub-manifold of a high dimensional ambient Euclidean space. The…

The transition from traditional power grids to smart grids, significant increase in the use of renewable energy sources, and soaring electricity prices has triggered a digital transformation of the energy infrastructure that enables new,…

Manifold learning techniques for nonlinear dimension reduction assume that high-dimensional feature vectors lie on a low-dimensional manifold, then attempt to exploit manifold structure to obtain useful low-dimensional Euclidean…

The study of neurocognitive tasks requiring accurate localisation of activity often rely on functional Magnetic Resonance Imaging, a widely adopted technique that makes use of a pipeline of data processing modules, each involving a variety…

Language grounding aims at linking the symbolic representation of language (e.g., words) into the rich perceptual knowledge of the outside world. The general approach is to embed both textual and visual information into a common space -the…

Despite their widespread success, the application of deep neural networks to functional data remains scarce today. The infinite dimensionality of functional data means standard learning algorithms can be applied only after appropriate…

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…

Using the concept of finite-size scaling, Monte Carlo calculations of various models have become a very useful tool for the study of critical phenomena, with the system linear dimension as a variable. As an example, several recent studies…

Functional data that are nonnegative and have a constrained integral can be considered as samples of one-dimensional density functions. Such data are ubiquitous. Due to the inherent constraints, densities do not live in a vector space and,…

Isometric feature mapping (Isomap) is a promising manifold learning method. However, Isomap fails to work on data which distribute on clusters in a single manifold or manifolds. Many works have been done on extending Isomap to…

Dimension reduction is often the first step in statistical modeling or prediction of multivariate spatial data. However, most existing dimension reduction techniques do not account for the spatial correlation between observations and do not…

Embedded spaces are a key feature in deep learning. Good embedded spaces represent the data well to support classification and advanced techniques such as open-set recognition, few-short learning and explainability. This paper presents a…

Time series classification problems have drawn increasing attention in the machine learning and statistical community. Closely related is the field of functional data analysis (FDA): it refers to the range of problems that deal with the…