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

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

Jul 18, 2023 538 likes •742 views

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 (Universit degli Studi di Padova) Super Carlo

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Li Link Prediction on Real and Sy Synthetic C c Comp mplex x Ne Networks

Department of Information Engineering 10/ 10/09/ 09/2018 2018 Ma Master Ca Candidate te: Umberto Michieli Super ervisors: Leonardo Badia (Università degli Studi di Padova) Carlo Cannistraci (Technische Universität Dresden)

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Topological Link k Predict

ction (L

(LP)

1

Problems: qLink forecast qPartial information qReconstruction Online social networks Biology Covert networks

A B C D E F

? ?

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Mo Moti tivati tion

2

LP LP me metho thods ds

Lo Local Gl Global

qMyt Myth h #1: global methods are better qMyt Myth h #2: SBM (global) should be the baseline qNo detailed LP test in the literature

Extensive LP evaluation

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LP LP Methods

3

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)

GL GLOB OBAL:

RA-L3 Resource Allocation on paths of length 3 (RA-L3) [Kovács et al. 2018]

[Muscoloni et al. 2018]

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Co Contr tributi tion

  • Sm

Small all-size vs. La Large-size

Re Real netwo works Synthetic c networks

  • Hy

Hyper erbol

  • lic 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

Standard procedure: remove 10% of links and compute

likelihood scores Mean precision, ranking and execution time

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SLIDE 6

Co Contr tributi tion

  • Sm

Small all-size vs. La Large-size

Re Real netwo works Synthetic c networks

  • Hy

Hyper erbol

  • lic 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)

4

Standard procedure: remove 10% of links and compute

likelihood scores Mean precision, ranking and execution time

SB SBM-bas based! d!!

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Sm Small-siz size Real al Networ

  • rks

Networks of disparate fields of study

5

Biology Transportation Food-web

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Sm Small-siz size Real al Networ

  • rks

# networks 25 # nodes 101 - 103

  • avg. density

0.24

  • avg. power-law exponent (γ)

4.22

SPM CH2-L2 SBM FBM RA-L3 SBM DC N SBM DC SBM N Mean precision

0. 0.34 34 0.30 0.28 0.27 0.26 0.22 0.21 0.06

Mean ranking

2. 2.1 2.9 3.6 4.1 4.3 5.2 6.1 7.9

Mean time

sec sec hours sec sec days hours days

5

✗ non scale-free ✗ non-hyperbolic

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Sm Small-siz size Real al Networ

  • rks

# networks 25 # nodes 101 - 103

  • avg. density

0.24

  • avg. power-law exponent (γ)

4.22

SPM CH2-L2 SBM FBM RA-L3 SBM DC N SBM DC SBM N Mean precision

0. 0.34 34 0.30 0.28 0.27 0.26 0.22 0.21 0.06

Mean ranking

2. 2.1 2.9 3.6 4.1 4.3 5.2 6.1 7.9

Mean time

sec sec hours sec sec days hours days

5

✗ non scale-free ✗ non-hyperbolic

Ø Confirmed also on 486 structural connectomes (82 nodes)

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La Large-siz size Real al Networ

  • rks

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Networks of disparate fields of study

Internet Online Social Networks Citation Lexical

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La Large-siz size Real al Networ

  • rks

ü scale-free

# networks 12 # nodes 103 to 104

  • avg. density

0.01

  • avg. power-law exponent (γ)

2.54

ü hyperbolic

CH2-L2

SPM Mean precision

0. 0.19 19

0.16 Mean ranking

1. 1.29 29

1.71 Mean time

0. 0.9 h

4.2 h

6

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Hyperbolic c Networks

1) 1) CH CH2-L2 L2 2) 2) SP SPM 3) 3) SB SBM 4) 4) FBM FBM

7

ØnP nPSO SO

N, m, T, γ=3

scale-free 100 iterations

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Eucl clidean Ne

Netw tworks (1/2)

ØConfirmed also on RGG

8

1) 1) SP SPM 2) 2) CH CH2-L2 L2 3) 3) FBM FBM 4) 4) SB SBM ØWS WS

N, m, β

non scale-free 100 iterations

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Eucl clidean Ne

Netw tworks (2/2)

9

scale-free 100 iterations

SBM-based ØLF LFR

N, m, μ, minc=N/10

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Eucl clidean Ne

Netw tworks (2/2)

1) 1) SP SPM 2) 2) CH CH2-L2 L2 3) 3) SB SBM M N 4) 4) FBM FBM

9

scale-free 100 iterations

SBM-based ØLF LFR

N, m, μ, minc=N/10

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Concl clusions

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

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Fu Futu ture W e Work

  • Enlarge dataset
  • CH2-L2, SPM and FBM on large-size networks
  • Model with adjustable hyperbolicity

11

  • Hybrid approach
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Thank you for the attention!