Application of neural networks to graph analysis with homophily and heterophily properties

Authors: Poikalainen A.M., Kochkarov R.A.

Introduction

Graph neural networks (GNNs) have become an important tool for analyzing structured data in areas such as recommender systems, bioinformatics, and anomaly detection. Traditional GNNs assume homophily, meaning that connected nodes have similar characteristics and labels. However, this limits their application in heterophily settings, where the connected nodes are different (Figure 1). We analyze the AMUD‑ADPA method [1]which improves the performance of GNN under homophily and heterophily using user activity data on a massive open online course (MOOC) platform [2].

Model AMUD-ADPA

The AMUD‑ADPA method consists of two components:

1. Adaptive Modeling of Undirected and Directed Graphs (AMUD)

2. Adaptive Directed Graph Aggregation (ADPA)

AMUD focuses on quantifying the relationship between nodes and graph topology, allowing adaptive decisions to consider edges as directed or undirected.

Adaptive Modeling of Undirected and Directed Graphs (AMUD) (Fig.2)

AMUD is a method that analyzes the graph topology and adaptively decides which links between nodes should be considered as directed and which should be considered as undirected. This approach is based on the following key steps:

— Relationship analysis: the graph structure and node characteristics are assessed to determine the type of relationships (homophilic or heterophilic).

— Adaptive solution: Depending on the identified characteristics, the links between nodes can be adapted to their type, which improves the accuracy of the models when classifying nodes.

Adaptive Directed Graph Aggregation (ADPA) (Fig. 3)

ADPA uses hierarchical attention mechanisms to aggregate information from a graph by adapting to its structure and the nature of its edges. The main steps of the ADPA process include:

— Attention mechanisms: ADPA uses attention mechanisms to determine the importance of different edges and nodes in the graph, allowing for more accurate consideration of the features of each node.

— Hierarchical aggregation: information is aggregated at different levels of the hierarchy, which provides a deeper understanding of the graph structure and improves the quality of classification.

The AMUD‑ADPA framework is particularly useful in applications such as:

— Recommender systems: Improve the accuracy of recommendations by taking into account complex interactions between the user and the element.

— Anomaly Detection: Identifying unusual patterns in dynamic networks, such as fraud detection in financial transactions.

— Social network analysis: Understanding the structure and dynamics of social interactions, especially in networks with diverse user behavior.

Experimental setup and results

To evaluate the AMUD-ADPA method, MOOC user action data representing user actions on an online course platform was used. Nodes represent users and course activities (goals), and edges represent user actions on goals. Actions have attributes and timestamps. Each action has a binary label indicating whether the user left the course after this action. Node characteristics include user engagement metrics and course activity characteristics.

Experiments were conducted on semi-supervised node classification problems, comparing baseline GNN models:

— GCN (Graph Convolutional Network) [3]

— GAT (Graph Attention Network) [4]

— GraphSAGE [5]

The results showed that AMUD‑ADPA outperforms traditional models in terms of accuracy, precision, recall and F1-score (Table 1, Fig. 4).

Table 1 Key performance indicators for model evaluation

Conclusion

The AMUD-ADPA method, developed to improve the performance of graph neural networks under homophily and heterophily, has proven its effectiveness on the MOOC dataset, outperforming baseline GNN models by 3.6% on average. The application of the AMUD-ADPA method can lead to more accurate and adaptive models for handling complex graph structures. This method opens up new possibilities for data analysis in areas such as recommender systems, where traditional methods are often insufficient. In the future, it is planned to develop a recommender system for students based on the analyzed AMUD-ADPA method trained on a new dataset of user interactions with an online education platform, which has a more complex structure than the MOOC dataset.