arXiv subjects

Amelia Simó

Publications and source records attributed to Amelia Simó.

8 recordsLinked to original sources

arXiv2026

A Python implementation of some geometric tools on Kendall 3D shape space for practical applications

This work addresses the challenge of analyzing geometric structures using Kendall's 3D Shape Space. While Riemannian geometry provides a robust framework for shape analysis (independent of scale, position, and orientation) the transition from theoretical manifolds to practical computational workflows remains difficult. Although Geomstats is currently the leading Python library for manifold-based statistics, it lacks specific utilities required for advanced 3D shape analysis. This article introduces tools designed to bridge this gap, translating complex mathematical abstractions into efficient, accessible software solutions for researchers.

stat.CO↗

arXiv2023

On using Reproducible Hilbert Spaces for the analysis of Replicated Spatial Point Processes

This paper focuses on the use of the theory of Reproducing Kernel Hilbert Spaces in the statistical analysis of replicated point processes. We show that spatial point processes can be observed as random variables in a Reproducing Kernel Hilbert Space and, as a result, methodological and theoretical results for statistical analysis in these spaces can be applied to them. In particular and by way of illustration, we show how we can use the proposed methodology to identify differences between several classes of replicate point patterns using the MBox and MANOVA tests, and to classify a new observation, using Discriminant Functions.

stat.ME↗

arXiv2022

Classification of geometrical objects by integrating currents and functional data analysis. An application to a 3D database of Spanish child population

This paper focuses on the application of Discriminant Analysis to a set of geometrical objects (bodies) characterized by currents. A current is a relevant mathematical object to model geometrical data, like hypersurfaces, through integration of vector fields along them. As a consequence of the choice of a vector-valued Reproducing Kernel Hilbert Space (RKHS) as a test space to integrate hypersurfaces, it is possible to consider that hypersurfaces are embedded in this Hilbert space. This embedding enables us to consider classification algorithms of geometrical objects. A method to apply Functional Discriminant Analysis in the obtained vector-valued RKHS is given. This method is based on the eigenfunction decomposition of the kernel. So, the novelty of this paper is the reformulation of a size and shape classification problem in Functional Data Analysis terms using the theory of currents and vector-valued RKHS. This approach is applied to a 3D database obtained from an anthropometric survey of the Spanish child population with a potential application to online sales of children's wear.

stat.ME↗

arXiv2021

A Review of Spatiotemporal Models for Count Data in R Packages. A Case Study of COVID-19 Data

Spatio-temporal models for count data are required in a wide range of scientific fields and they have become particularly crucial nowadays because of their ability to analyse COVID-19-related data. Models for count data are needed when the variable of interest take only non-negative integer values and these integers arise from counting occurrences. Several R-packages are currently available to deal with spatiotemporal areal count data. Each package focuses on different models and/or statistical methodologies. Unfortunately, the results generated by these models are rarely comparable due to differences in notation and methods. The main objective of this paper is to present a review describing the most important approaches that can be used to model and analyse count data when questions of scientific interest concern both their spatial and their temporal behaviour and we monitor their performance under the same data set. For this review, we focus on the three R-packages that can be used for this purpose and the different models assessed are representative of the two most widespread methodologies used to analyse spatiotemporal count data: the classical approach (based on Penalised Likelihood or Estimating Equations) and the Bayesian point of view. A case study is analysed as an illustration of these different methodologies. In this case study, these packages are used to model and predict daily hospitalisations from COVID-19 in 24 health regions within the Valencian Community (Spain), with data corresponding to the period from 28 June to 13 December 2020. Because of the current urgent need for monitoring and predicting data in the COVID-19 pandemic, this case study is, in itself, of particular importance and can be considered the secondary objective of this work. Satisfactory and promising results have been obtained in this second goal.

stat.AP↗

arXiv2018

Generalized Linear Models for Geometrical Current predictors. An application to predict garment fit

The aim of this paper is to model an ordinal response variable in terms of vector-valued functional data included on a vector-valued RKHS. In particular, we focus on the vector-valued RKHS obtained when a geometrical object (body) is characterized by a current and on the ordinal regression model. A common way to solve this problem in functional data analysis is to express the data in the orthonormal basis given by decomposition of the covariance operator. But our data present very important differences with respect to the usual functional data setting. On the one hand, they are vector-valued functions, and on the other, they are functions in an RKHS with a previously defined norm. We propose to use three different bases: the orthonormal basis given by the kernel that defines the RKHS, a basis obtained from decomposition of the integral operator defined using the covariance function, and a third basis that combines the previous two. The three approaches are compared and applied to an interesting problem: building a model to predict the fit of children's garment sizes, based on a 3D database of the Spanish child population.

stat.AP↗

arXiv2018

Generalized partially linear models on Riemannian manifolds

The generalized partially linear models on Riemannian manifolds are introduced. These models, like ordinary generalized linear models, are a generalization of partially linear models on Riemannian manifolds that allow for response variables with error distribution models other than a normal distribution. Partially linear models are particularly useful when some of the covariates of the model are elements of a Riemannian manifold, because the curvature of these spaces makes it difficult to define parametric models. The model was developed to address an interesting application, the prediction of children's garment fit based on 3D scanning of their body. For this reason, we focus on logistic and ordinal models and on the important and difficult case where the Riemannian manifold is the three-dimensional case of Kendall's shape space. An experimental study with a well-known 3D database is carried out to check the goodness of the procedure. Finally it is applied to a 3D database obtained from an anthropometric survey of the Spanish child population. A comparative study with related techniques is carried out.

stat.ME↗

arXiv2016

Unsupervised classification of children's bodies using currents

Object classification according to their shape and size is of key importance in many scientific fields. This work focuses on the case where the size and shape of an object is characterized by a current}. A current is a mathematical object which has been proved relevant to the modeling of geometrical data, like submanifolds, through integration of vector fields along them. As a consequence of the choice of a vector-valued Reproducing Kernel Hilbert Space (RKHS) as a test space for integrating manifolds, it is possible to consider that shapes are embedded in this Hilbert Space. A vector-valued RKHS is a Hilbert space of vector fields; therefore, it is possible to compute a mean of shapes, or to calculate a distance between two manifolds. This embedding enables us to consider size-and-shape classification algorithms. These algorithms are applied to a 3D database obtained from an anthropometric survey of the Spanish child population with a potential application to online sales of children's wear.

stat.ME↗

arXiv2014

Inhomogeneous K-function for germ-grain models

In this paper, we propose a generalization to germ-grain models of the inhomogeneous K-function of Point Processes. We apply them to a sample of images of peripheral blood smears obtained from patients with Sickle Cell Disease, in order to decide whether the sample belongs to the thin, thick or morphological region.

stat.OT↗