Comparing High Order Networks by Persistence Homology
نویسندگان
چکیده
This paper presents methods to compare high order networks using persistence homology. High order networks induce well-founded homological features and the difference between networks is measured by the difference between the homological features. This is a reasonable approximation to a valid metric in the space of high order networks modulo permutation isomorphisms. The approximations succeed in identifying collaboration patterns of engineering and math academic journals.
منابع مشابه
Persistent Path Homology of Directed Networks Samir Chowdhury and Facundo Mémoli
While standard persistent homology has been successful in extracting information from metric datasets, its applicability to more general data, e.g. directed networks, is hindered by its natural insensitivity to asymmetry. We extend a construction of homology of digraphs due to Grigoryan, Lin, Muranov and Yau to the persistent framework. The result, which we call persistent path homology or PPH,...
متن کاملPersistent Homology of Asymmetric Networks: an Approach Based on Dowker Filtrations
We propose methods for computing two network features with topological underpinnings: the Rips and Dowker Persistent Homology Diagrams. Our formulations work for general networks, which may be asymmetric and may have any real number as an edge weight. We study the sensitivity of Dowker persistence diagrams to intrinsic asymmetry in the data, and investigate the stability properties of both the ...
متن کاملConvergence of Hierarchical Clustering and Persistent Homology Methods on Directed Networks
While there has been much interest in adapting conventional clustering procedures—and in higher dimensions, persistent homology methods—to directed networks, little is known about the convergence of such methods. In order to even formulate the problem of convergence for such methods, one needs to stipulate a reasonable model for a directed network together with a flexible sampling theory for su...
متن کاملCosheaf Theoretical Constructions in Networks and Persistent Homology
In this paper, we study data flows in directed networks with a hierarchical recurrent structure from a cosheaf theoretical perspective. We utilize the visual parametrization of directed recurrent programs provided in persistence diagrams for cosheaf theoretical constructions. In considering cosheaves on persistence diagrams, we link global network structure and local recurrent process data. An ...
متن کاملStable Signatures for Dynamic Metric Spaces via Zigzag Persistent Homology
When studying flocking/swarming behaviors in animals one is interested in quantifying and comparing the dynamics of the clustering induced by the coalescence and disbanding of animals in different groups. Motivated by this, we study the problem of obtaining persistent homology based summaries of time-dependent metric data. Given a finite dynamic metric space (DMS), we construct the zigzag simpl...
متن کامل