KENNESAW, Ga. | Oct 27, 2026

By Mehmet Aktas, Ph.D.

Modern organizations generate enormous amounts of connected data. Customers interact with products, employees collaborate with one another, patients move through healthcare systems, users participate in online communities, and consumers engage with digital content in many different ways. These relationships are often more informative than the individual data points themselves. This is where graph-based analytics can provide a powerful perspective: instead of asking only what we know about an individual entity, we can ask how that entity is connected to everything around it.

My research focuses on developing mathematical and machine learning methods for reasoning over these complex networks. A particular focus of my work is the use of sheaf theory and sheaf-based graph learning to model situations in which different relationships carry different meanings. Traditional graph models often treat connections in similar ways, but a “likes,” “dislikes,” “purchases,” or “collaborates-with” relationship does not necessarily convey the same type of information. Sheaf-based models provide a mathematical framework for preserving these differences and determining how information should propagate across a network.

One important application of this idea is context-aware ranking and expertise detection. In online knowledge communities, for example, identifying the most knowledgeable person is not always enough. A user may be highly knowledgeable about one topic but have limited expertise in another. In our work on crowdsourcing platforms such as Stack Exchange, we developed sheaf Laplacian–based diffusion models that identify experts at the subtopic level using users' interactions and the topics associated with their contributions. Rather than producing one global ranking, the approach can answer more useful questions such as: Who are the most knowledgeable users about a particular topic?

This same idea extends naturally to business applications. Consider customer analytics: a customer may be highly engaged with one product category but uninterested in another. Similarly, an employee may be an expert in one area of an organization but not another. A graph-based model that understands the context of relationships can therefore produce more useful rankings and recommendations than a model that assigns every entity with a single global score.

We have also applied sheaf-based network models to healthcare provider evaluation. By representing healthcare providers as a network based on shared patients and incorporating provider specialties, we developed methods for ranking providers according to both their network position and the relevance of their clinical expertise. This illustrates an important advantage of graph-based reasoning: performance can be evaluated in the context of the broader system rather than in isolation.

More recently, our work has extended sheaf-based ranking to multiple attributes and higher-order interactions. Instead of asking only which entity is most important, we can ask which entity is most important with respect to a particular attribute or context. This perspective has direct relevance to recommendation systems. A recommendation is fundamentally a ranking problem, but the “best” recommendation depends on the user, the user's preferences, and the context. Our previous work on attribute-aware sheaf ranking provides a foundation for developing recommendation models that can account for these differences.

The next step in this research is to move from graph analytics toward graph-based reasoning. Rather than using a graph simply to improve prediction, we seek to use the structure and semantics of the graph to understand why information is propagated, which signals are consistent, and where conflicting information originates. Our emerging work combines sheaf-based graph learning with ontologies—formal representations of concepts and relationships—to create models that can incorporate semantic knowledge directly into graph reasoning.

This direction is particularly promising for personalization and recommendation. Imagine a system that does not simply recommend a movie because its latent representation is similar to a user's history, but can explain that recommendation through meaningful relationships: the user has positively engaged with several science-fiction films, those films share particular actors or franchises, and the recommended film is connected through those same concepts. At the same time, the system could identify conflicting signals. For example, a user's explicit dislike of a genre despite repeated engagement with related content.

The broader goal is to develop graph-based AI systems that are not only predictive but also context-aware, explainable, and capable of reasoning over heterogeneous information. This perspective has applications well beyond entertainment recommendation. It can support customer segmentation, expert identification, healthcare analytics, organizational networks, social media analysis, fraud detection, and other business problems where relationships and context matter.

Graph analytics tells us that connections matter. Graph-based reasoning asks us what those connections mean, how information should flow through them, and whether the resulting conclusions are consistent. I believe this transition, from analyzing graphs to reasoning over graphs, represents an important direction for the next generation of data-driven decision systems.