Tenzorske reprezentacije hipergrafa i primjene u analizi društvenih mreža

Mihaljević, Mate (2014) Tenzorske reprezentacije hipergrafa i primjene u analizi društvenih mreža. Diploma thesis, Faculty of Science > Department of Mathematics.

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Abstract

In this work we presented basic definitions related with tensors. Specified description is made for notation and tensor operations. We also observed determination of tensor rank and differences in comparation between property of tensor and matrix rank (tensor rank can be different over $\mathbb{R}$ and over $\mathbb{C}$, the problem of determining tensor rank is NP-hard). After that this work deals with determining PARAFAC tensor decomposition of third-order tensors, while for the higher-order tensors is presented pseudocode on Figure 1.7. Also, in this work we presented TweetRank, a novel approach for authority ranking in SocialWeb communities. Conceptually, TweetRank is a correspondent to authority ranking methods known from Web retrieval, such as PageRank or HITS. This approach exploits the novel representational model for social graphs, based on 3-dimensional tensors. This allows us to exploit in the natural way the available semantics of user relations. By applying the PARAFAC tensor decomposition we identify authoritative sources in the social network as well as groups of semantically coherent terms of interest. Therefore, TweetRank can be seen as a next step towards efficient and effective search/recommendation technology for the Social Web.

Item Type: Thesis (Diploma thesis)
Supervisor: Grubišić, Luka
Date: 2014
Number of Pages: 37
Subjects: NATURAL SCIENCES > Mathematics
Divisions: Faculty of Science > Department of Mathematics
Depositing User: Iva Prah
Date Deposited: 05 Jun 2015 11:16
Last Modified: 05 Jun 2015 11:16
URI: http://digre.pmf.unizg.hr/id/eprint/4015

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