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Immagine del redattoreAndrea Viliotti

GRAF: A New Approach for the Fusion of Heterogeneous Networks

In the context of analyzing large volumes of data, heterogeneous networks represent a significant challenge. These networks include different types of nodes and relationships, making it difficult to apply machine learning tools designed for homogeneous networks, composed of only one type of node and relationship. The research presented by Ziynet Nesibe Kesimoglu and Serdar Bozdag, affiliated respectively with the Departments of Computer Science, Mathematics, and BioDiscovery Institute at the University of North Texas, introduces GRAF (Graph Attention-aware Fusion Networks), a framework that allows heterogeneous and multiplex networks to be transformed into homogeneous networks for more effective analysis through Graph Representation Learning techniques.

GRAF: A New Approach for the Fusion of Heterogeneous Networks
GRAF: A New Approach for the Fusion of Heterogeneous Networks

Complex Networks: Heterogeneous, Multiplex, and Multi-Omic

The growing complexity of data in the real world has necessitated the use of advanced network models capable of representing intricate relationships between different entities. Among these models, heterogeneous, multiplex, and multi-omic networks stand out for their ability to capture the dynamics of complex systems, offering powerful and detailed representations.


Heterogeneous networks are characterized by the integration of multiple types of nodes and relationships in a single graph. This makes them ideal for representing scenarios where the entities involved belong to different categories, such as interactions between proteins, diseases, and drugs. Each node and each connection represent distinct elements, creating a complex ecosystem that can be analyzed to identify significant cross-connections. Their versatility is particularly useful in fields like computational biology and recommendation systems, where the diversity of relationships is crucial for obtaining more comprehensive insights.


Multiplex networks, on the other hand, introduce a layered structure that allows different types of relationships between the same set of nodes to be represented. Each layer of the network describes a specific type of interaction, maintaining a clear distinction between relationships. This model is particularly useful when connections between entities are of a different nature and should not be mixed into a single representation. A practical example is the world of social media, where personal, professional, and shared-interest relationships can be analyzed separately, yet always connected through shared nodes.


Multi-omic networks represent a specific application of heterogeneous and multiplex networks in the field of biology and medicine. These networks integrate data from various omic disciplines, such as genomics, transcriptomics, proteomics, and epigenomics, to analyze biological complexity in a holistic manner. Each level of the network captures a unique aspect of the biological system, and their fusion allows the discovery of interactions across different molecular scales that would otherwise remain hidden. For example, the combined analysis of genomic and proteomic data can reveal new biomarkers for complex diseases, providing a deeper understanding of pathological mechanisms.


Despite differences in structure and application, all these networks share a common goal: to represent complexity in a way that can be understood, analyzed, and exploited. The choice of the most suitable model depends on the nature of the data and the objectives of the analysis. Heterogeneous networks offer a unified overview, multiplex networks allow a layered analysis of interactions, and multi-omic networks provide an integrated framework to study multidimensional biological systems. This makes these models fundamental for tackling the challenges of data-driven decision-making in increasingly complex scientific and industrial sectors.


The Challenges of Multiplex and Heterogeneous Networks

Real-world networks are often composed of multiple types of nodes and connections, such as authors, articles, and conferences, each with different relationships like publication or participation. This type of heterogeneity poses significant challenges for traditional Graph Neural Networks (GNNs), primarily designed for homogeneous networks with only one type of node and connection. Multiplex networks, which contain different types of relationships (e.g., author-article and article-conference relationships), introduce additional complexities when attempting to model them.


In particular, managing heterogeneous and multiplex networks requires addressing the multiplicity of associations and the heterogeneity of nodes. Each layer of the multiplex network represents a subgraph with connections of a specific type. Converting a heterogeneous network into a homogeneous multiplex network requires the use of metapaths, which connect nodes through defined types of relationships. This process allows measuring the similarity between start and end nodes, enabling the model to treat a heterogeneous network as a combination of homogeneous subnetworks.


Current methodologies based on GNNs face significant challenges when applied separately to each layer of the multiplex network. For example, approaches like MOGONET and SUPREME use Graph Convolutional Networks (GCN) on each layer of the multiplex network and then integrate the label distributions from each layer to determine the final label of the nodes. However, this process is computationally expensive and becomes quickly impractical when the number of layers increases, as often occurs in multi-omic data contexts. Additionally, traditional models tend not to consider node and relationship-specific attention, which can limit the overall effectiveness of the model.


To overcome these limitations, GRAF uses a network fusion approach based on attention mechanisms, applying attention at both the node and network layer levels. This allows greater importance to be attributed to the most influential relationships and nodes that are most relevant to the prediction task. In practice, the node-level attention mechanism allows different weights to be assigned to each neighboring node based on its relevance, while the network layer-level attention allows evaluating the importance of the different types of connections present in the network.


GRAF not only converts heterogeneous networks into a more manageable structure for learning but also uses a process of eliminating connecting edges between nodes to reduce complexity and improve model effectiveness. After network fusion, some edges are removed depending on their weight, thereby retaining only the most significant connections. This step is crucial to reduce the density of the network and increase accuracy in predictions.


Finally, GRAF stands out for its ability to provide interpretable results through the use of attention weights, which allow identifying critical network components for the prediction task. These weights make it possible to explain why certain nodes or layers are more influential, improving the model's transparency and reliability. The results show that the use of multi-level attention enables GRAF to outperform existing methodologies for both heterogeneous and multiplex networks, demonstrating remarkable robustness and generalizability.


The GRAF Solution

GRAF was designed to address these issues by using an attention-based network fusion mechanism to obtain a single homogeneous network. The fusion is divided into several steps:


  1. Generation of Multiplex Networks: If the initial network is heterogeneous, GRAF converts it into a multiplex network using metapaths, which allow homogeneous subnetworks to be created that represent the type of relationship analyzed. For example, in the case of the IMDB dataset, two metapaths (MRM and MDM) were used to represent relationships between movies, actors, and directors, creating a multiplex network for nodes of the movie type. Similarly, for the ACM dataset, metapaths were used to connect articles, authors, and research topics, allowing the construction of homogeneous multiplex networks reflecting the different relationships present.


  2. Attention Calculation: GRAF applies an attention mechanism at both the node and network layer levels to determine the importance of neighboring nodes and relationships (layers) present in the network. This process is fundamental to assign different weights to connections based on their relevance. Specifically, GRAF calculates two types of attention: node-level attention and network layer-level attention. These values are then used to weigh the importance of each connection in the fused network. Experimental results have shown that node-level and layer-level attention significantly improve model performance, as evidenced by an ablation study on the datasets used. For example, on IMDB, GRAF achieved a macro F1 score (a metric used to evaluate the performance of classification models) of 62.1%, outperforming other approaches like SUPREME and GCN.


  3. Network Fusion: Using the attention weights calculated, GRAF fuses the various layers of the network into a single weighted network, subsequently removing weak links that may not contribute significantly to the prediction task. The network fusion process is based on a weighted aggregation of edges from the various layers using the previously calculated attention values. For each pair of nodes, GRAF sums the weights of the existing edges in the different layers, weighting them according to the importance of the layer and the node. This approach creates a network representation that retains only the most significant connections for the task at hand. Additionally, an edge elimination step is included to further reduce network complexity. Experiments have shown that retaining 70% of the original edges in the ACM and DBLP datasets, and 30% for the DrugADR dataset, improves the quality of predictions.


  4. Node Classification: On the fused network, GRAF uses a GCN to generate node embeddings and then perform a prediction task, such as node classification.


Applications and Results

GRAF has been applied to four different datasets from various domains, each with specific characteristics and challenges. In the case of the IMDB dataset (heterogeneous graph for the movie industry), the network was converted using two metapaths: Movie-Actor-Movie (MAM) and Movie-Director-Movie (MDM), transforming the initial heterogeneous network into a multiplex network for movie-type nodes. This approach enabled GRAF to operate more efficiently and accurately than traditional methods, outperforming algorithms like GCN, GAT, and SUPREME in terms of macro F1 score, achieving a score of 62.1%, higher than GCN's 58.7% and GAT's 56.8%.


In the ACM dataset (heterogeneous graph for bibliometric analysis), GRAF was used for classifying types of scientific articles. The heterogeneous network, composed of articles, authors, and subjects, was converted using the metapaths Paper-Author-Paper (PAP) and Paper-Subject-Paper (PSP). GRAF achieved a macro F1 score of 92.6%, slightly higher than SUPREME's 92.4% and GCN's 91.5%. This highlights how node-level and network layer-level attention improves the classification ability of the model compared to conventional approaches.


For the DBLP dataset (heterogeneous graph for scientific publication analysis), relating to the prediction of authors' research areas, four metapaths were used: Author-Paper-Author (APA), Author-Paper-Author-Paper-Author (APAPA), Author-Paper-Conference-Paper-Author (APCPA), and Author-Paper-Term-Paper-Author (APTPA). GRAF achieved a macro F1 score of 91.7%, outperforming models like GATv2 (90.0%) and GCN (90.5%). This demonstrates its efficiency in integrating complex multi-relational information.


For adverse drug reaction prediction in the DrugADR dataset (heterogeneous graph for pharmacological analysis and adverse reactions), GRAF integrated four distinct network layers based on chemical similarities and drug interaction data. The model achieved a macro F1 score of 34.7%, surpassing SUPREMEmax's 32.1% and HAN's 30.2%. These results highlight GRAF's effectiveness in dealing with particularly complex datasets, such as biological and medical ones, where the ability to integrate different types of relationships is key to improving prediction accuracy.


Thanks to its attention-based fusion architecture, GRAF was able not only to improve prediction quality but also to maintain good generalizability across multiple application domains, making it an effective tool for analyzing heterogeneous and multiplex networks.


The Importance of Attention Mechanisms

In the DrugADR dataset, the analysis of attention weights revealed that networks based on the similarity of side effects and chemical structures of drugs were the most influential for predicting adverse reactions. Specifically, the network based on the similarity of side effects obtained the highest attention weights, indicating that this type of information was crucial for determining the prediction outcome.


In the ACM dataset, the network constructed using the metapath Paper-Author-Paper (PAP) showed significantly higher attention compared to the metapath Paper-Subject-Paper (PSP). This suggests that co-authorship information between articles has a greater impact on thematic area classification than subject-based information. The average attention weight for the PAP metapath was greater than 0.6, indicating a strong correlation with prediction success.


In the DBLP dataset, the network layer built using the metapath Author-Paper-Conference-Paper-Author (APCPA) received the highest attention weights, highlighting how the conferences at which papers are presented are a determining factor in classifying an author's research area.


Ablation studies conducted to verify the importance of attention mechanisms further confirmed their crucial role. Selectively removing node-level or layer-level attention significantly decreased the model's performance. The GRAFnet_lay variant, which used only layer-level attention, recorded a macro F1 score of 56.3% on the IMDB dataset, compared to the 62.1% of the full version of GRAF. Similarly, the GRAFnode variant, which considered only node-level attention, achieved a macro F1 score of 61.3%, lower than the complete model but higher than GRAFnet_lay, highlighting how both types of attention are essential for the model's effectiveness.


Moreover, the GRAFedge variant, which used both node-level and layer-level attention without edge elimination, achieved comparable performance to the complete GRAF model, with a macro F1 score of 62.1% on IMDB and 33.9% on DrugADR, demonstrating that selective edge elimination, while useful, is not as crucial as integrating both types of attention.


The metrics used to evaluate the performance of GRAF and its variants include macro F1 score, weighted F1 score, and accuracy, calculated over 10 repetitions for each dataset. The macro F1 score, in particular, highlighted how GRAF manages to outperform most state-of-the-art (SOTA) approaches and baseline methods.


The implementation of attention mechanisms in GRAF not only improves prediction accuracy but also provides greater model interpretability. Attention weights allow identifying the nodes and relationships that contribute most to the success of the prediction task, making GRAF a powerful and transparent tool for analyzing complex networks. Eliminating weak edges during network fusion further contributed to reducing complexity, improving the model's generalizability across different domains.


Future Implications

The future implications of GRAF are vast and extend to many fields where heterogeneous networks play a key role. One of the most promising sectors is life sciences and healthcare. For example, the DrugADR dataset showed that integrating chemical similarity networks and clinical data through GRAF can improve the prediction of adverse drug reactions. With a macro F1 score of 34.7%, GRAF demonstrated how integrating various sources of heterogeneous data can provide a more complete and accurate view of potential drug side effects. This approach could be further developed for clinical applications, such as personalizing therapies and identifying optimal drug combinations for patients.


Another field of application concerns academic research and bibliometrics. The use of GRAF for classifying scientific articles in the ACM dataset showed that node-level attention, such as co-authorship, is fundamental for correctly classifying the topic. The metapath Paper-Author-Paper (PAP) suggests that networks based on relationships between authors can provide critical information for understanding the thematic structure of academic research. This could be further extended to identify emerging trends in research or to map potential collaborations between researchers in different fields.


The social network field could also benefit from GRAF's capabilities to handle heterogeneous data. Modern social networks consist of multiple types of nodes (e.g., users, posts, hashtags) and relationships (friendships, mentions, likes). Using GRAF in this context could help identify key influencers, predict information diffusion, or detect anomalous behavior. GRAF's ability to manage complex networks and fuse multiple layers of information could significantly improve the analysis of social dynamics.


Finally, the field of economics and financial networks represents another area of application. Financial networks are inherently heterogeneous, with nodes representing financial entities, transactions, and credit relationships. Applying GRAF in this field could improve the ability to detect fraudulent behavior, assess financial risk, or predict market trends. Integrating data from various sources, such as relationships between financial institutions and historical market behavior, could provide more robust and reliable predictive models.


In conclusion, the potential of GRAF, and in general of models using attention mechanisms and network fusion, is broad and promising. Future expansion of this approach could include applying it to more complex and larger datasets, as well as optimizing attention mechanisms to further reduce computational costs. GRAF's generalizability across different domains suggests that the model could become a fundamental tool for tackling complex problems where interactions between different entities must be deeply understood.


Conclusions

The proposal of GRAF offers an interesting strategic perspective for the analysis and use of heterogeneous and multiplex networks in increasingly data-complex environments. The ability to transform heterogeneous structures into homogeneous and interpretable representations highlights a paradigm shift in managing complex information, which finds cross-sectional applications from medicine to finance, from social media to academic research. However, the implications of this model are not limited to improving analytical performance. GRAF embodies a response to the growing need for AI systems that are not only effective but also provide transparency and interpretive capacity.


The attention mechanism that distinguishes GRAF from other approaches opens a new chapter in understanding complex data, emphasizing a strategic priority: the importance of assigning meaning and weight to critical connections rather than treating all data uniformly. This has significant consequences for organizations operating in high-density informational environments, as it highlights the need for models capable of separating relevant signals from noise, optimizing both the use of computational resources and decision quality.


The fusion of networks with the elimination of weak edges, for instance, is not just a computational technique but a philosophical principle that can be applied on multiple levels. Recognizing the uselessness of some connections—which may seem important in a local context but prove irrelevant on a global scale—is a fundamental lesson for any complex organizational system. Similarly, multi-level attention introduces a layered decision model that can guide companies in managing priorities: which nodes (resources, clients, markets) are crucial and which can be left in the background?


Another key element is the potential impact on the integration and valorization of multi-source data. In an era where information silos are one of the main barriers to innovation, GRAF shows how the convergence of information from heterogeneous domains can unlock insights that would otherwise remain inaccessible. For companies, this means not only improving analytical efficiency but also redefining the boundaries of innovation: cross-interactions, such as those between genomic and proteomic data in medicine, or between professional relationships and topics in academia, become fertile ground for new discoveries and strategies.


Finally, the interpretability of the results, made possible by attention weights, is not only a technical advantage but represents a growing requirement in regulated and high-impact social sectors. The ability to explain model predictions introduces fundamental trust, both for organizations and external stakeholders, paving the way for greater adoption of AI solutions in sensitive contexts. This is particularly relevant in areas like healthcare, where decisions based on predictive models must be justifiable to ensure acceptance by patients and authorities.


In an increasingly technologically integrated world, GRAF offers a broader lesson: complexity is not an obstacle but an opportunity to rethink decision-making models, finding new ways to give meaning to connections and build smarter and more adaptive systems. For companies, this means adopting a mindset that not only embraces data diversity but makes it the core of their ability to innovate and compete. GRAF's approach is not just an analytical methodology: it is a metaphor for the future of business strategy in an increasingly connected and interdependent world.



 

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