Related papers: A Geometric Perspective on Sparse Filtrations

Sparse decomposition has been widely used for different applications, such as source separation, image classification and image denoising. This paper presents a new algorithm for segmentation of an image into background and foreground text…

In many applications it is important to estimate a fluid flow field from limited and possibly corrupt measurements. Current methods in flow estimation often use least squares regression to reconstruct the flow field, finding the…

Evolution of 3D graphics and graphical worlds has brought issues like content optimization, real-time processing, rendering, and shared storage limitation under consideration. Generally, different simplification approaches are used to make…

An efficient computer algorithm is described for the perspective drawing of a wide class of surfaces. The class includes surfaces corresponding lo single-valued, continuous functions which are defined over rectangular domains. The algorithm…

We consider several basic questions pertaining to the geometry of image of a general quadratic map. In general the image of a quadratic map is non-convex, although there are several known classes of quadratic maps when the image is convex.…

We consider offsets of a union of convex objects. We aim for a filtration, a sequence of nested cell complexes, that captures the topological evolution of the offsets for increasing radii. We describe methods to compute a filtration based…

Many practical applications in topological data analysis arise from data in the form of point clouds, which then yield simplicial complexes. The combinatorial structure of simplicial complexes captures the topological relationships between…

Classical filtrations in probability theory formalize the accumulation of information along a linear time axis: the past is unique and the present evolves into an uncertain future. In reality, however, this linearity may itself be an…

The aim of this paper is to present an original approach that takes advantage from the geometric features of strictly convex functions to tackle the problem of finding the minimum from another perspective. The general idea is that near the…

Visual insights into a wide variety of statistical methods, for both didactic and data analytic purposes, can often be achieved through geometric diagrams and geometrically based statistical graphs. This paper extols and illustrates the…

In this survey, we explore recent literature on finding the cores of higher graphs using geometric and topological means. We study graphs, hypergraphs, and simplicial complexes, all of which are models of higher graphs. We study the notion…

We propose an algorithm to estimate the topology of an embedded metric graph from a well-sampled finite subset of the underlying graph.

In topological data analysis (TDA), a longstanding challenge is to recognize underlying geometric structures in noisy data. One motivating examples is the shape of a point cloud in Euclidean space given by image. Carlsson et al. proposed a…

We propose sparseGeoHOPCA, a novel framework for sparse higher-order principal component analysis (SHOPCA) that introduces a geometric perspective to high-dimensional tensor decomposition. By unfolding the input tensor along each mode and…

Sparse feature selection has been demonstrated to be effective in handling high-dimensional data. While promising, most of the existing works use convex methods, which may be suboptimal in terms of the accuracy of feature selection and…

Square contingency tables are traditionally analyzed with a focus on the symmetric structure of the corresponding probability tables. We view probability tables as elements of a simplex equipped with the Aitchison geometry. This perspective…

This paper describes a method for fast simplification of surface meshes. Whereas past methods focus on visual appearance, our goal is to solve equations on the surface. Hence, rather than approximate the extrinsic geometry, we construct a…

Recent advances in optimizing Gaussian Splatting for scene geometry have enabled efficient reconstruction of detailed surfaces from images. However, when input views are sparse, such optimization is prone to overfitting, leading to…

Decomposition techniques for linear programming are difficult to extend to conic optimization problems with general non-polyhedral convex cones because the conic inequalities introduce an additional nonlinear coupling between the variables.…

The present paper attempts to show an alternative approach with regards to rational Pythagorean-hodograph (PH) curves and especially more natural approach for rational PH helices (i.e. rational helices). It exploits geometric features of…