Related papers: On Geometric Prototype And Applications

The network embedding problem aims to map nodes that are similar to each other to vectors in a Euclidean space that are close to each other. Like centrality analysis (ranking) and community detection, network embedding is in general…

This paper deals with the geometric multi-model fitting from noisy, unstructured point set data (e.g., laser scanned point clouds). We formulate multi-model fitting problem as a sequential decision making process. We then use a deep…

In this work, we propose to study the global geometrical properties of generative models. We introduce a new Riemannian metric to assess the similarity between any two data points. Importantly, our metric is agnostic to the parametrization…

We present a geometric formulation of the Multiple Kernel Learning (MKL) problem. To do so, we reinterpret the problem of learning kernel weights as searching for a kernel that maximizes the minimum (kernel) distance between two convex…

This paper presents a geometric approach to the classical isoperimetric problem by analysing the efficiency of regular polygons in enclosing maximum area for a fixed perimeter. Using efficiency metrics, it proves that regular polygons…

Geometric modeling by constraints, whose applications are of interest to communities from various fields such as mechanical engineering, computer aided design, symbolic computation or molecular chemistry, is now integrated into standard…

In the era of foundation models and Large Language Models (LLMs), Euclidean space has been the de facto geometric setting for machine learning architectures. However, recent literature has demonstrated that this choice comes with…

The use of geometric and symmetry techniques in quantum and classical information processing has a long tradition across the physical sciences as a means of theoretical discovery and applied problem solving. In the modern era, the emergent…

Given two sets of points $A$ and $B$ in a normed plane, we prove that there are two linearly separable sets $A'$ and $B'$ such that $\mathrm{diam}(A')\leq \mathrm{diam}(A)$, $\mathrm{diam}(B')\leq \mathrm{diam}(B)$, and $A'\cup B'=A\cup B.$…

We present an algorithm to compute the geometric median of shapes which is based on the extension of median to high dimensions. The median finding problem is formulated as an optimization over distances and it is solved directly using the…

This paper is aimed at presenting a systematic survey of the existing now different formulations for the problem of projection of the origin of the Euclidean space onto the convex polyhedron (PPOCP). In the present paper, there are…

A many-body Hamiltonian can be block-diagonalized by expressing it in terms of symmetry-adapted basis states. Finding the group orbit representatives of these basis states and their corresponding symmetries is currently a…

Finding correspondences between shapes is a fundamental problem in computer vision and graphics, which is relevant for many applications, including 3D reconstruction, object tracking, and style transfer. The vast majority of correspondence…

The problem of finding suitable point embedding or geometric configurations given only Euclidean distance information of point pairs arises both as a core task and as a sub-problem in a variety of machine learning applications. In this…

We introduce hybrid classical-quantum algorithms for problems involving a large classical data set X and a space of models Y such that a quantum computer has superposition access to Y but not X. These algorithms use data reduction…

A homotopy method for multi-objective optimization that produces uniformly sampled Pareto fronts by construction is presented. While the algorithm is general, of particular interest is application to simulation-based engineering…

This paper studies the parameter tuning problem of positive linear systems for optimizing their stability properties. We specifically show that, under certain regularity assumptions on the parametrization, the problem of finding the…

We prove that some exact geometric pattern matching problems reduce in linear time to $k$-SUM when the pattern has a fixed size $k$. This holds in the real RAM model for searching for a similar copy of a set of $k\geq 3$ points within a set…

Distributed optimization algorithms are widely used in many industrial machine learning applications. However choosing the appropriate algorithm and cluster size is often difficult for users as the performance and convergence rate of…

Large collections of high-dimensional data have become nearly ubiquitous across many academic fields and application domains, ranging from biology to the humanities. Since working directly with high-dimensional data poses challenges, the…