Applied Mathematics & Information Sciences

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Manifolds are suitable differentiable mathematical objects for information to be defined on. By their very definition they are non-Euclidean in the global view but in local scales they resemble Euclidean spaces. This property provides that the contemporary information models can also be defined within the previsioned new models of information models. One of the most basic representations of information is through graphs. They are discrete and highly computable mathematical objects. In this research, the main aim is to investigate methods of embedding this simple piece of information onto manifolds. This research shows that the very fundamental data structures of computer science can be transformed into the continuous spaces and wide area of applications can be engineered such as pattern recognition or anomaly detection. The visualizations of the inspected methods are the evidence of that the graph data can carry new characteristics other than classical properties of graphs such as curvature, locality or multi-dimensionality.

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