Related papers: spd-metrics-id: A Python Package for SPD-Aware Dis…
In this project, we introduce OPESCI-FD, a Python package built on symbolic mathematics to automatically generate Finite Difference models from a high-level description of the model equations. We investigate applying this framework to…
Symmetric positive definite (SPD) matrices arising from functional connectivity analysis of neuroimaging data can be endowed with a Riemannian geometric structure that standard methods fail to respect. While existing R packages provide some…
Representing images and videos with Symmetric Positive Definite (SPD) matrices and considering the Riemannian geometry of the resulting space has proven beneficial for many recognition tasks. Unfortunately, computation on the Riemannian…
metric-learn is an open source Python package implementing supervised and weakly-supervised distance metric learning algorithms. As part of scikit-learn-contrib, it provides a unified interface compatible with scikit-learn which allows to…
Shape-constrained nonparametric regression is a growing area in econometrics, statistics, operations research, machine learning and related fields. In the field of productivity and efficiency analysis, recent developments in the…
There is a strong recent emphasis on trustworthy AI. In particular, international regulations, such as the AI Act, demand that AI practitioners measure data quality on the input and estimate bias on the output of high-risk AI systems.…
Persistence diagrams (PD)s play a central role in topological data analysis, and are used in an ever increasing variety of applications. The comparison of PD data requires computing comparison metrics among large sets of PDs, with metrics…
We introduce the Push-Forward Signed Distance Morphometric (PF-SDM) for shape quantification in biomedical imaging. The PF-SDM compactly encodes geometric and topological properties of closed shapes, including their skeleton and symmetries.…
Metric learning has been shown to be highly effective to improve the performance of nearest neighbor classification. In this paper, we address the problem of metric learning for Symmetric Positive Definite (SPD) matrices such as covariance…
Qualifying the discrepancy between 3D geometric models, which could be represented with either point clouds or triangle meshes, is a pivotal issue with board applications. Existing methods mainly focus on directly establishing the…
The need for efficiently comparing and representing datasets with unknown alignment spans various fields, from model analysis and comparison in machine learning to trend discovery in collections of medical datasets. We use manifold learning…
Existing multimodal stress/pain recognition approaches generally extract features from different modalities independently and thus ignore cross-modality correlations. This paper proposes a novel geometric framework for multimodal…
Automated data-driven modeling, the process of directly discovering the governing equations of a system from data, is increasingly being used across the scientific community. PySINDy is a Python package that provides tools for applying the…
We propose the use of the vector-valued distance to compute distances and extract geometric information from the manifold of symmetric positive definite matrices (SPD), and develop gyrovector calculus, constructing analogs of vector space…
New and upgraded radio interferometers produce data at massive rates and will require significant improvements in analysis techniques to reach their promised levels of performance in a routine manner. Until these techniques are fully…
We introduce Geomstats, an open-source Python toolbox for computations and statistics on nonlinear manifolds, such as hyperbolic spaces, spaces of symmetric positive definite matrices, Lie groups of transformations, and many more. We…
Generating consistent and high-quality images from given texts is essential for visual-language understanding. Although impressive results have been achieved in generating high-quality images, text-image consistency is still a major concern…
A non-vector-based dissimilarity measure is proposed by combining vector-based distance metrics and set operations. This proposed compound dissimilarity measure (CDM) is applicable to quantify similarity of collections of attribute/feature…
We explore the connection between two problems that have arisen independently in the signal processing and related fields: the estimation of the geometric mean of a set of symmetric positive definite (SPD) matrices and their approximate…
The Python package pylimer-tools is a comprehensive toolkit for computational studies of polymer networks, particularly bead-spring networks. The package provides functionality to generate polymer networks using Monte Carlo (MC) procedures…