Link Prediction on Real and Li Sy Synthetic C c Comp mplex x - PowerPoint PPT Presentation

Link Prediction on Real and Li Sy Synthetic C c Comp mplex x Ne Networks Department of Information Engineering Ma Master Ca Candidate te: Umberto Michieli ervisors: Leonardo Badia (Università degli Studi di Padova) Super Carlo Cannistraci (Technische Universität Dresden) 10/09/ 10/ 09/2018 2018

k Predict ction (L Topological Link (LP) C Problems: ? A B q Link forecast ? D q Partial information F E q Reconstruction Online social Biology Covert networks networks 1

Mo Moti tivati tion LP LP me metho thods ds Global Gl Local Lo h #1 : global methods are better q Myt Myth h #2 : SBM (global) should be the baseline q Myt Myth q No detailed LP test in the literature Extensive LP evaluation 2

LP Methods LP GL GLOB OBAL: SPM Structural Perturbation Method [Lü et al. 2015] SBM Stochastic Block Model (SBM) [Guimerà et al. 2009] FBM Fast probability Block Model (FBM) [Liu et al. 2013] DC SBM Degree Corrected SBM (DC SBM) [Karrer et al. 2011] N SBM Nested SBM (N SBM) [Peixoto 2014] DC N SBM DC and N SBM [Peixoto 2014] LOCAL CAL: CH2-L2 Second variation of Cannistraci-Hebb on paths of length 2 (CH2-L2) [Muscoloni et al. 2018] RA-L3 Resource Allocation on paths of length 3 (RA-L3) [Kovács et al. 2018] 3

Co Contr tributi tion Standard procedure: remove 10% of links and compute likelihood scores Mean precision, ranking and execution time Re Real netwo works all -size vs. La Large -size • Sm Small Synthetic c networks • Hy Hyper erbol olic g geom eometr etry : nonuniform Popularity- Similarity-Optimization (nPSO) • Euc Euclide lidean an geometry : Watts-Strogatz (WS), Random Geometric Graph (RGG), Lancichinetti-Fortunato- Radicchi (LFR) 4

Co Contr tributi tion Standard procedure: remove 10% of links and compute likelihood scores Mean precision, ranking and execution time Re Real netwo works all -size vs. La Large -size • Sm Small Synthetic c networks • Hy Hyper erbol olic g geom eometr etry : nonuniform Popularity- Similarity-Optimization (nPSO) • Euc Euclide lidean an geometry : Watts-Strogatz (WS), Random Geometric Graph (RGG), La Lancichinetti-Fo Fortunato- Ra Radicch cchi (L (LFR FR) SBM-bas SB based! d!! 4

Sm Small-siz size Real al Networ orks Networks of disparate fields of study Biology Transportation Food-web 5

Sm Small-siz size Real al Networ orks # networks 25 10 1 - 10 3 # nodes ✗ non-hyperbolic avg. density 0.24 ✗ non scale-free avg. power-law exponent (γ) 4.22 SPM CH2-L2 SBM FBM RA-L3 SBM DC N SBM DC SBM N Mean 0.30 0.28 0.27 0.26 0.22 0.21 0.06 0. 0.34 34 precision Mean 2.9 3.6 4.1 4.3 5.2 6.1 7.9 2.1 2. ranking Mean sec sec hours sec sec days hours days time 5

Small-siz Sm size Real al Networ orks # networks 25 10 1 - 10 3 # nodes ✗ non-hyperbolic avg. density 0.24 ✗ non scale-free avg. power-law exponent (γ) 4.22 SPM CH2-L2 SBM FBM RA-L3 SBM DC N SBM DC SBM N Mean 0.30 0.28 0.27 0.26 0.22 0.21 0.06 0. 0.34 34 precision Mean 2.9 3.6 4.1 4.3 5.2 6.1 7.9 2. 2.1 ranking Mean sec sec hours sec sec days hours days time Ø Confirmed also on 486 structural connectomes (82 nodes) 5

La Large-siz size Real al Networ orks Networks of disparate fields of study Online Social Networks Internet Citation Lexical 6

La Large-siz size Real al Networ orks # networks 12 10 3 to 10 4 # nodes avg. density 0.01 ü hyperbolic avg. power-law exponent (γ) 2.54 ü scale-free CH2-L2 SPM 0. 0.19 19 Mean precision 0.16 1. 1.29 29 Mean ranking 1.71 0. 0.9 h Mean time 4.2 h 6

Hyperbolic c Networks Ø nP nPSO SO N, m, T, γ=3 scale-free 100 iterations 1) 1) CH CH2-L2 L2 2) 2) SP SPM 3) 3) SB SBM 4) 4) FBM FBM 7

Eucl clidean Ne Netw tworks (1/2) Ø WS WS N, m, β non scale-free 100 iterations 1) SP 1) SPM 2) 2) CH CH2-L2 L2 3) 3) FBM FBM 4) 4) SB SBM Ø Confirmed also on RGG 8

Eucl clidean Ne Netw tworks (2/2) Ø LF LFR N, m, μ, minc=N/10 scale-free 100 iterations SBM-based 9

Eucl clidean Ne Netw tworks (2/2) Ø LF LFR N, m, μ, minc=N/10 scale-free 100 iterations SBM-based 1) 1) SP SPM 2) CH 2) CH2-L2 L2 3) 3) SB SBM M N 4) 4) FBM FBM 9

Concl clusions SPM & CH2-L2 are better baseline than SBM Extensive LP test Loca cal organization can be as effective as global 10

Fu Futu ture W e Work • Enlarge dataset • CH2-L2, SPM and FBM on large-size networks • Model with adjustable hyperbolicity • Hybrid approach 11

Thank you for the attention!