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Construction of the Vietoris-Rips simplicial complex

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

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    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: 52
    Language of Content: Slovenian
    Mentor / Comentors:
    Name and SurnameIDFunction
    prof. dr. Neža Mramor Kosta242Mentor
    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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