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Cybercrime Prediction via Geographically Weighted Learning

Muhammad Al-Zafar Khan, Jamal Al-Karaki, Emad Mahafzah

TL;DR

Results show that GeogGNN has higher accuracy than standard neural networks and convolutional neural networks, which treat the coordinates as features, and is a powerful tool for handling complex, geographically distributed data.

Abstract

Inspired by the success of Geographically Weighted Regression and its accounting for spatial variations, we propose GeogGNN -- A graph neural network model that accounts for geographical latitude and longitudinal points. Using a synthetically generated dataset, we apply the algorithm for a 4-class classification problem in cybersecurity with seemingly realistic geographic coordinates centered in the Gulf Cooperation Council region. We demonstrate that it has higher accuracy than standard neural networks and convolutional neural networks that treat the coordinates as features. Encouraged by the speed-up in model accuracy by the GeogGNN model, we provide a general mathematical result that demonstrates that a geometrically weighted neural network will, in principle, always display higher accuracy in the classification of spatially dependent data by making use of spatial continuity and local averaging features.

Cybercrime Prediction via Geographically Weighted Learning

TL;DR

Results show that GeogGNN has higher accuracy than standard neural networks and convolutional neural networks, which treat the coordinates as features, and is a powerful tool for handling complex, geographically distributed data.

Abstract

Inspired by the success of Geographically Weighted Regression and its accounting for spatial variations, we propose GeogGNN -- A graph neural network model that accounts for geographical latitude and longitudinal points. Using a synthetically generated dataset, we apply the algorithm for a 4-class classification problem in cybersecurity with seemingly realistic geographic coordinates centered in the Gulf Cooperation Council region. We demonstrate that it has higher accuracy than standard neural networks and convolutional neural networks that treat the coordinates as features. Encouraged by the speed-up in model accuracy by the GeogGNN model, we provide a general mathematical result that demonstrates that a geometrically weighted neural network will, in principle, always display higher accuracy in the classification of spatially dependent data by making use of spatial continuity and local averaging features.

Paper Structure

This paper contains 6 sections, 3 theorems, 14 equations, 8 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Theory: Geographically Weighted Graph Neural Networks (GeogGNNs)
  4. Experiments
  5. Mathematical Analysis
  6. Conclusion

Key Result

Lemma 1

(Spatial continuity of $h^{*}$). Let $\left(L,d\right)$ be a metric space endowed with the Euclidean notion of distance, i.e., $d=||\ell-\ell'||$ for $\ell,\ell'\in L$. Then, points that are geographically close (often) belong to the same class, and $h^{*}$ varies smoothly over $L$.

Figures (8)

  • Figure 1: Loss function and confusion matrix for the model for the GeogGNN model.
  • Figure 2: ROC and PR curves for each class in the model GeogGNN model.
  • Figure 3: Loss function and training and validation accuracy for the standard neural network model.
  • Figure 4: Precision-recall curves for the standard neural network model.
  • Figure 5: Confusion matrix and ROC curves for the standard neural network model.
  • ...and 3 more figures

Theorems & Definitions (13)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Definition 5
  • Definition 6
  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • ...and 3 more