Comparing persistence diagrams through complex vectors

Di Fabio, Barbara ; Ferri, Massimo (2015) Comparing persistence diagrams through complex vectors. [Preprint]
Full text available as:
[img]
Preview
PDF
License: Creative Commons Attribution Non-commercial

Download (943kB) | Preview

Abstract

The natural pseudo-distance of spaces endowed with filtering functions is precious for shape classification and retrieval; its optimal estimate coming from persistence diagrams is the bottleneck distance, which unfortunately suffers from combinatorial explosion. A possible algebraic representation of persistence diagrams is offered by complex polynomials; since far polynomials represent far persistence diagrams, a fast comparison of the coefficient vectors can reduce the size of the database to be classified by the bottleneck distance. This article explores experimentally three transformations from diagrams to polynomials and three distances between the complex vectors of coefficients.

Abstract
Document type
Preprint
Creators
CreatorsAffiliationORCID
Di Fabio, Barbara
Ferri, Massimo
Keywords
Persistence diagram, shape analysis, Vi`ete formulas, precision, recall
Subjects
DOI
Deposit date
27 Apr 2015 12:28
Last modified
28 Oct 2015 15:00
URI

Other metadata

Downloads

Downloads

Staff only: View the document

^