Beyond Topological Persistence: Starting from Networks

نویسندگان

چکیده

Persistent homology enables fast and computable comparison of topological objects. We give some instances a recent extension the theory persistence, guaranteeing robustness computability for relevant data types, like simple graphs digraphs. focus on categorical persistence functions that allow us to study in full generality strong kinds connectedness—clique communities, k-vertex, k-edge connectedness—directly connectedness

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Topological Persistence and Simplification

We formalize a notion of topological simplification within the framework of a filtration, which is the history of a growing complex. We classify a topological change that happens during growth as either a feature or noise depending on its lifetime or persistence within the filtration. We give fast algorithms for computing persistence and experimental evidence for their speed and utility.

متن کامل

Image Segmentation Using Topological Persistence

This paper presents a new hybrid split-and-merge image segmentation method based on computational geometry and topology using persistent homology. The algorithm uses edge-directed topology to initially split the image into a set of regions based on the Delaunay triangulations of the points in the edge map. Persistent homology is used to generate three types of regions: p-persistent regions, p-t...

متن کامل

Topological Persistence in Jacobi Sets

This report is generated as a result of work done by this author in the IMA’s New Directions: Computational Topology course. The purpose of the paper is to discuss results of one of the problems given by the course leaders to the participants. The problem given was to investigate the concept of topological persistence when computing Jacobi sets of a pair of real-valued functions f, g defined on...

متن کامل

Instantons beyond Topological Theory Ii

The present paper is the second part of our project in which we describe quantum field theories with instantons in a novel way by using the " infinite radius limit " (rather than the limit of free field theory) as the starting point. The theory dramatically simplifies in this limit, because the correlation functions of all, not only topological (or BPS), observables may be computed explicitly i...

متن کامل

A persistence landscapes toolbox for topological statistics

Topological data analysis provides a multiscale description of the geometry and topology of quantitative data. The persistence landscape is a topological summary that can be easily combined with tools from statistics and machine learning. We give efficient algorithms for calculating persistence landscapes, their averages, and distances between such averages. We discuss an implementation of thes...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Mathematics

سال: 2021

ISSN: ['2227-7390']

DOI: https://doi.org/10.3390/math9233079