A Variance-aware Multiobjective Louvain-like Method for Community Detection in Multiplex Networks

This repository contains the codes of the paper "A Variance-aware Multiobjective Louvain-like Method for Community Detection in Multiplex Networks" by Sara Venturini, Andrea Cristofari, Francesco Rinaldi, Francesco Tudisco.

Proposed Methods

• GL: Generalized Louvain (in particular: in GL_s communities are indexed by size and in GL_r are indexed randomly).
• EVM: Louvain Expansion Method Function F-.
• EVP: Louvain Expansion Method Function F+.
• MA: Louvain Multiobjective Method Average (in particular: in MA_s communities are indexed by size and in MA_r are indexed randomly).
• MVM: Louvain Multiobjective Method Function F-.
• MVP: Louvain Multiobjective Method Function F+.

State-of-the-art methods (to be added in this folder)

Download

• From https://github.com/youweiliang/Multi-view_Clustering: Co-Regularized Spectral Clustering (CoReg), multi-view clustering via Adaptively Weighted Procrustes (AWP), Multi-view Consensus Graph Clustering (MCGC), and The Power Mean Laplacian Multi-layer Method (PM).
• From https://github.com/cdebacco/MultiTensor: Multitensor expectation maximization method (MT).
• From https://github.com/gilles-didier/MolTi: Subspace Analysis on Grassmann Manifolds (SCML), and Principal Modularity Maximization (PMM).
• From https://github.com/mapequation/infomap: Infomap Information-theoretic generalization of mapequation (IM).

Help files

• INFOMAP_adjacency_matrix: from adjecency matrix to input file IM method.
• MULTITENSOR_adjacency_matrix: from adjecency matrix to input file for MT method.

Artificial networks

SBM Stochastic Block Model

• adjacent_matrix_generator: creates a single-layer graph using the Stochastic Block Model
• adjacent_matrix_generator_multi: creates a multi-layer graph for the informative case: each layer is informative. Each layer is created by the adjacent_matrix_generator. -adjacent_matrix_generator_multi_r: creates a multi-layer graph for the noisy case: SOME layer noisy and SOME layers informative. Each layer is created by the adjacent_matrix_generator.

LFR Lancichinetti-Fortunato-Radicchi

From https://www.santofortunato.net/resources Package 1
A. Lancichinetti, S. Fortunato, and F. Radicchi, Benchmark graphs for testing community detection algorithms, Physical review E, vol. 78, no. 4, p. 046110, 2008.

Real Datasets

From https://github.com/melopeo/PM_SSL/tree/master/realworld_datasets
P. Mercado, F. Tudisco, and M. Hein, Generalized Matrix Means for Semi-Supervised Learning with Multilayer Graphs. In NeurIPS 2019.

Evaluation of the final partitions

• confusion_matrix: calculates the confusion matrix. It is used in "wrong" function and input of "NMI" function.
• reindex_com: reindexes communities. It is used in "confusion_matrix" function.
• wrong: counts the number of nodes in the wrong community. It is used to calculate the Accuracy of a partition.
• NMI: calculates the Normalized Mutual Information (NMI) of a partition.

Tests on Artificial Networks

SBM

test_ART: run all the artificial tests SBM (informative and real) reported in the paper.

• run: tests each methods on artificial networks SBM for the informative case.
• run_n: tests each methods on artificial networks SBM for the noisy case.

LFR

test_ART_LFR: run all the artificial tests LFR (informative and real) reported in the paper.

• run_LFR: tests each methods on artificial networks LFR for the informative case .
• run_n_LFR: tests each methods on artificial networks LFR for the noisy case.

Tests on Real Datasets

test_REAL: run all the tests on real-world networks (informative and real) reported in the paper.

• REAL: tests each methods on real datasets.
• REAL_n2: tests each methods on real datasets with noise (all informative layers + one noisy layer).
• REAL_n3: tests each methods on real datasets with noise (first layer sum of all the real layers, second layer is noise).

Reference paper

"A Variance-aware Multiobjective Louvain-like Method for Community Detection in Multiplex Networks" by Sara Venturini, Andrea Cristofari, Francesco Rinaldi, Francesco Tudisco.

Authors

• Sara Venturini (e-mail: sara.venturini@math.unipd.it)
• Andrea Cristofari (e-mail: andrea.cristofari@unipd.it)
• Francesco Rinaldi (e-mail: rinaldi@math.unipd.it)
• Francesco Tudisco (e-mail: francesco.tudisco@gssi.it)