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Discriminative community detection for multiplex networks

Meiby Ortiz-Bouza, Selin Aviyente

TL;DR

Two discriminative community detection algorithms based on spectral clustering are introduced, which aims to identify the discriminative subgraph structure between the groups, while the second one learns the discriminative and the consensus community structures, simultaneously.

Abstract

Multiplex networks have emerged as a promising approach for modeling complex systems, where each layer represents a different mode of interaction among entities of the same type. A core task in analyzing these networks is to identify the community structure for a better understanding of the overall functioning of the network. While different methods have been proposed to detect the community structure of multiplex networks, the majority deal with extracting the consensus community structure across layers. In this paper, we address the community detection problem across two closely related multiplex networks. For example in neuroimaging studies, it is common to have multiple multiplex brain networks where each layer corresponds to an individual and each group to different experimental conditions. In this setting, one may be interested in both learning the community structure representing each experimental condition and the discriminative community structure between two groups. In this paper, we introduce two discriminative community detection algorithms based on spectral clustering. The first approach aims to identify the discriminative subgraph structure between the groups, while the second one learns the discriminative and the consensus community structures, simultaneously. The proposed approaches are evaluated on both simulated and real world multiplex networks.

Discriminative community detection for multiplex networks

TL;DR

Two discriminative community detection algorithms based on spectral clustering are introduced, which aims to identify the discriminative subgraph structure between the groups, while the second one learns the discriminative and the consensus community structures, simultaneously.

Abstract

Multiplex networks have emerged as a promising approach for modeling complex systems, where each layer represents a different mode of interaction among entities of the same type. A core task in analyzing these networks is to identify the community structure for a better understanding of the overall functioning of the network. While different methods have been proposed to detect the community structure of multiplex networks, the majority deal with extracting the consensus community structure across layers. In this paper, we address the community detection problem across two closely related multiplex networks. For example in neuroimaging studies, it is common to have multiple multiplex brain networks where each layer corresponds to an individual and each group to different experimental conditions. In this setting, one may be interested in both learning the community structure representing each experimental condition and the discriminative community structure between two groups. In this paper, we introduce two discriminative community detection algorithms based on spectral clustering. The first approach aims to identify the discriminative subgraph structure between the groups, while the second one learns the discriminative and the consensus community structures, simultaneously. The proposed approaches are evaluated on both simulated and real world multiplex networks.
Paper Structure (20 sections, 17 equations, 4 figures, 1 table)

This paper contains 20 sections, 17 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Related Work
  3. Background
  4. Graph clustering and subspace representation
  5. Multiplex Network Community Detection
  6. Discriminative Community Detection Methods
  7. Multiplex Discriminative Spectral Clustering (MX-DSC)
  8. Multiplex Discriminative and Consensus Spectral Clustering (MX-DCSC)
  9. Finding the embedding dimensions
  10. Subgraph Identification
  11. Computational Complexity
  12. Experiments
  13. Synthetic Multiplex Networks
  14. Evaluation
  15. Experiment 1: Varying Noise Level, $\mu$
  16. ...and 5 more sections

Figures (4)

  • Figure 1: Overview of the proposed methods. Discriminative embedding matrices are learned for each group, $\mathbf{\bar{U}}_1$ and $\mathbf{\bar{U}}_2$. $k$-means with $k=2$ is applied to the degrees of $|\mathbf{Z}_1|$ and $|\mathbf{Z}_2|$ to separate the nodes in the shared and in the discriminative subspace, respectively.
  • Figure 2: NMI Results for MX-DCSC with respect to other methods: (a) Experiment 1, (b) Experiment 2, (c) Experiment 3
  • Figure 3: Discriminative Communities for Error (left) and Correct (right) responses.
  • Figure 4: UCI Handwritten dataset results. Images that were selected as (a) discriminative and (b) shared nodes for both groups (digits 1 and 7).