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Centrality-Based Node Feature Augmentation for Robust Network Alignment

Jin-Duk Park, Cong Tran, Won-Yong Shin, Xin Cao

TL;DR

Grad-Align+ exhibits the superiority over benchmark NA methods, empirical validations as well as theoretical findings to see the effectiveness of CNFA, the influence of each component, the robustness to network noises, and the computational efficiency.

Abstract

Network alignment (NA) is the task of discovering node correspondences across multiple networks. Although NA methods have achieved remarkable success in a myriad of scenarios, their effectiveness is not without additional information such as prior anchor links and/or node features, which may not always be available due to privacy concerns or access restrictions. To tackle this challenge, we propose Grad-Align+, a novel NA method built upon a recent state-of-the-art NA method, the so-called Grad-Align, that gradually discovers a part of node pairs until all node pairs are found. In designing Grad-Align+, we account for how to augment node features in the sense of performing the NA task and how to design our NA method by maximally exploiting the augmented node features. To achieve this goal, Grad-Align+ consists of three key components: 1) centrality-based node feature augmentation (CNFA), 2) graph neural network (GNN)-aided embedding similarity calculation alongside the augmented node features, and 3) gradual NA with similarity calculation using aligned cross-network neighbor-pairs (ACNs). Through comprehensive experiments, we demonstrate that Grad-Align+ exhibits (a) the superiority over benchmark NA methods, (b) empirical validations as well as our theoretical findings to see the effectiveness of CNFA, (c) the influence of each component, (d) the robustness to network noises, and (e) the computational efficiency.

Centrality-Based Node Feature Augmentation for Robust Network Alignment

TL;DR

Grad-Align+ exhibits the superiority over benchmark NA methods, empirical validations as well as theoretical findings to see the effectiveness of CNFA, the influence of each component, the robustness to network noises, and the computational efficiency.

Abstract

Network alignment (NA) is the task of discovering node correspondences across multiple networks. Although NA methods have achieved remarkable success in a myriad of scenarios, their effectiveness is not without additional information such as prior anchor links and/or node features, which may not always be available due to privacy concerns or access restrictions. To tackle this challenge, we propose Grad-Align+, a novel NA method built upon a recent state-of-the-art NA method, the so-called Grad-Align, that gradually discovers a part of node pairs until all node pairs are found. In designing Grad-Align+, we account for how to augment node features in the sense of performing the NA task and how to design our NA method by maximally exploiting the augmented node features. To achieve this goal, Grad-Align+ consists of three key components: 1) centrality-based node feature augmentation (CNFA), 2) graph neural network (GNN)-aided embedding similarity calculation alongside the augmented node features, and 3) gradual NA with similarity calculation using aligned cross-network neighbor-pairs (ACNs). Through comprehensive experiments, we demonstrate that Grad-Align+ exhibits (a) the superiority over benchmark NA methods, (b) empirical validations as well as our theoretical findings to see the effectiveness of CNFA, (c) the influence of each component, (d) the robustness to network noises, and (e) the computational efficiency.
Paper Structure (42 sections, 4 theorems, 20 equations, 12 figures, 5 tables, 2 algorithms)

This paper contains 42 sections, 4 theorems, 20 equations, 12 figures, 5 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Background and Motivation
  3. Main Contributions
  4. Methodology
  5. Network Model and Basic Assumptions
  6. Problem Definition
  7. Overview of Grad-Align+
  8. Proposed Method: Grad-Align+
  9. Methodological Details of Grad-Align+
  10. CNFA
  11. GNN-Based Embedding Similarity Calculation
  12. Gradual NA with ACN Similarity Calculation
  13. Theoretical Analysis
  14. Expressiveness Analysis of Augmented Node Features
  15. Influence of CNFA on Vector Representations
  16. ...and 27 more sections

Key Result

Theorem 3.1

Suppose that $\phi$, $g$, and $f_w$ are all injective. We also assume that a mapping function between a node degree and a color label in the WL test is injective. Then, when degree centrality is adopted in CNFA, in the $l$-th GNN layer, the expressive power of $\mathbf{\hat{h}}_{u,*}^{(l)}$ is highe

Figures (12)

  • Figure 1: Alignment accuracy (a) for the scenario where a portion of prior anchor links vary on Facebook vs. Twitter and (b) for the scenario with and without node features on Douban Online vs. Douban Offline.
  • Figure 2: An example illustrating a naïve NFA approach for NA. Here, (a,A) and (b,B) are ground truth cross-network node pairs, and the red dashed curves denote the (incorrectly) discovered node correspondences via NA.
  • Figure 3: The schematic overview of our Grad-Align+ method.
  • Figure 4: Examples illustrating inconsistent node features based on (a) Katz centrality and (b) degree centrality. The structurally consistent area is highlighted in yellow.
  • Figure 5: An instance that describes two networks $G_s$ and $G_t$ to be aligned. Here, the red dashed line denotes a matched node pair (c,C) in the first iteration of gradual NA.
  • ...and 7 more figures

Theorems & Definitions (7)

  • Definition 2.1: NA
  • Theorem 3.1
  • Theorem 3.2
  • Theorem 3.1
  • proof
  • Theorem 3.2
  • proof