Construction of the Vietoris-Rips simplicial complex

Leonard Štefančič (2013) Construction of the Vietoris-Rips simplicial complex. EngD thesis.

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Abstract

In the thesis simplicial complexes as a means for representing topological spaces are presented. In particular, the Vietoris-Rips complex, which is used in computer science for data reconstruction and analysis, is described. A two-phase algorithm for constructing the Vietoris-Rips complex on a given data set is described. In the first phase, the algorithms constructs the neighborhood graph on a set of points, and in the second phase the graph is extended to a simplicial complex. Three approaches, inductive, incremental and maximal, for the second phase are described and proofs of their correctness are given. The algorithms are tested on an example, and their efficiency is analyzed.

Item Type:

Thesis (EngD thesis)

Keywords:

k-simplex, simplicial complex, Vietoris-Rips complex, neighborhood graph, clique complex

Number of Pages:

Language of Content:

Slovenian

Mentor / Comentors:

Name and Surname	ID	Function
prof. dr. Neža Mramor Kosta	242	Mentor

Link to COBISS:

http://www.cobiss.si/scripts/cobiss?command=search&base=50070&select=(ID=9959508)

Institution:

University of Ljubljana

Department:

Faculty of Computer and Information Science

Item ID:

2057

Date Deposited:

19 Jun 2013 16:03

Last Modified:

16 Jul 2013 09:07

URI:

http://eprints.fri.uni-lj.si/id/eprint/2057

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