Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

A generalized motif-based Naïve Bayes model for sign prediction in complex networks

Yijun Ran, Si-Yuan Liu, Junjie Huang, Tao Jia, Xiao-Ke Xu

TL;DR

This work tackles sign prediction in signed networks by addressing the limitation of equal-neighbor influence in motif-based Naïve Bayes models. It introduces GSMNB-CL and GSMNB-CN to capture heterogeneous neighbor effects and extends to multiple motifs with GMMNB and FGMNB, the latter leveraging a machine-learning classifier on motif-derived features. Across four real networks, FGMNB yields the strongest AUC on three datasets, outperforming several embedding-based baselines, while GSMNB-CL consistently surpasses SMNB, underscoring the value of incorporating common-link information. The results demonstrate that local motif structures drive predictive power in sign prediction, offering a transparent, effective alternative to deep embeddings with practical implications for trust and security in online platforms.

Abstract

Signed networks, encoding both positive and negative interactions, are essential for modeling complex systems in social and financial domains. Sign prediction, which infers the sign of a target link, has wide-ranging practical applications. Traditional motif-based Naïve Bayes models assume that all neighboring nodes contribute equally to a target link's sign, overlooking the heterogeneous influence among neighbors and potentially limiting performance. To address this, we propose a generalizable sign prediction framework that explicitly models the heterogeneity. Specifically, we design two role functions to quantify the differentiated influence of neighboring nodes. We further extend this approach from a single motif to multiple motifs via two strategies. The generalized multiple motifs-based Naïve Bayes model linearly combines information from diverse motifs, while the Feature-driven Generalized Motif-based Naïve Bayes (FGMNB) model integrates high-dimensional motif features using machine learning. Extensive experiments on four real-world signed networks show that FGMNB consistently outperforms five state-of-the-art embedding-based baselines on three of these networks. Moreover, we observe that the most predictive motif structures differ across datasets, highlighting the importance of local structural patterns and offering valuable insights for motif-based feature engineering. Our framework provides an effective and theoretically grounded solution to sign prediction, with practical implications for enhancing trust and security in online platforms.

A generalized motif-based Naïve Bayes model for sign prediction in complex networks

TL;DR

This work tackles sign prediction in signed networks by addressing the limitation of equal-neighbor influence in motif-based Naïve Bayes models. It introduces GSMNB-CL and GSMNB-CN to capture heterogeneous neighbor effects and extends to multiple motifs with GMMNB and FGMNB, the latter leveraging a machine-learning classifier on motif-derived features. Across four real networks, FGMNB yields the strongest AUC on three datasets, outperforming several embedding-based baselines, while GSMNB-CL consistently surpasses SMNB, underscoring the value of incorporating common-link information. The results demonstrate that local motif structures drive predictive power in sign prediction, offering a transparent, effective alternative to deep embeddings with practical implications for trust and security in online platforms.

Abstract

Signed networks, encoding both positive and negative interactions, are essential for modeling complex systems in social and financial domains. Sign prediction, which infers the sign of a target link, has wide-ranging practical applications. Traditional motif-based Naïve Bayes models assume that all neighboring nodes contribute equally to a target link's sign, overlooking the heterogeneous influence among neighbors and potentially limiting performance. To address this, we propose a generalizable sign prediction framework that explicitly models the heterogeneity. Specifically, we design two role functions to quantify the differentiated influence of neighboring nodes. We further extend this approach from a single motif to multiple motifs via two strategies. The generalized multiple motifs-based Naïve Bayes model linearly combines information from diverse motifs, while the Feature-driven Generalized Motif-based Naïve Bayes (FGMNB) model integrates high-dimensional motif features using machine learning. Extensive experiments on four real-world signed networks show that FGMNB consistently outperforms five state-of-the-art embedding-based baselines on three of these networks. Moreover, we observe that the most predictive motif structures differ across datasets, highlighting the importance of local structural patterns and offering valuable insights for motif-based feature engineering. Our framework provides an effective and theoretically grounded solution to sign prediction, with practical implications for enhancing trust and security in online platforms.
Paper Structure (20 sections, 22 equations, 5 figures, 5 tables)

This paper contains 20 sections, 22 equations, 5 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Network-embedding methods
  4. Feature-based methods
  5. Problem definition
  6. Methodology
  7. Network motifs
  8. Single motif-based Naïve Bayes model
  9. Generalized single motif-based Naïve Bayes model
  10. Generalized multiple motifs-based Naïve Bayes model
  11. Time complexity analysis
  12. XGBoost classifier
  13. Experiments and analysis
  14. Network data
  15. Experimental setup
  16. ...and 5 more sections

Figures (5)

  • Figure 1: The ten network motifs and nine different predictors. A) We consider ten unique 3-node and 4-node motifs in an undirected signed network. B) The nine predictors are derived from distinct 3-node and 4-node motifs. Each predictor $S_\text{i}$ includes a red line representing the target link whose sign needs to be predicted. For 3-node predictors $S_\text{i}$, we quantify the heterogeneous influence of the neighboring node $C$ on the positive or negative sign of link $(A, B)$. For 4-node predictors $S_\text{i}$, we treat the neighboring link $(C, D)$ as a single entity and evaluate the heterogeneous influence of the neighboring link $(C, D)$ on the sign of link $(A, B)$.
  • Figure 2: An example demonstrating the different contributions of node $M$ to the probability of links $(A, B)$ and $(E, F)$ having positive or negative signs. For predictor $S_\text{1}$, there are four predictors, $S_\text{1}(A, M, C)$, $S_\text{1} (B, M, D)$, $S_\text{1}(C, M, E)$, and $S_\text{1} (D, M, F)$, formed with the node $M$. For the target link $(A, B)$, links $(A, M)$ and $(B, M)$ appear in $S_\text{1}(A, M, C)$ and $S_\text{1} (B, M, D)$, respectively, however $S_\text{1}(D, M, F)$ and $S_\text{1}(C, M, E)$ only involve the node $M$ and exclude the links $(A, M)$ and $(B, M)$. For the target link (E, F), links $(E, M)$ and $(F, M)$ appear in $S_\text{1}(C, M, E)$ and $S_\text{1} (D, M, F)$, respectively, while $S_\text{1}(A, M, C)$ and $S_\text{1}(B, M, D)$ only involve the node $M$ and exclude the links $(E, M)$ and $(F, M)$.
  • Figure 3: The complete description of two role functions. A) All possible predictors $S_\text{1}$ formed with the node $M$. These predictors can be utilized in two ways. B) One is to consider the predictors $S_\text{1}$ formed with the node $M$ in which each predictor $S_\text{1}$ includes at least one of the links $(A, M)$ and $(B, M)$. C) The other is to consider the predictors $S_\text{1}$ formed with the node $M$ where each predictor includes only node $M$ and excludes the links $(A, M)$ and $(B, M)$.
  • Figure 4: The Relationship Between Motif Coverage and Algorithm Performance (AUC). The sign prediction performance of different algorithms, particularly GSMNB-CL, shows a positive correlation with motif coverage. Specifically, as the motif coverage of a given motif type increases within the network, the corresponding AUC also tends to increase.
  • Figure 5: The Receiver Operating Characteristic (ROC) curves for FGMNB. The ROC curves demonstrate a pronounced rise above the diagonal baseline, reflecting the FGMNB’s strong discriminative capability.