  Geodesic distances on manifolds have numerous applications in image
processing, computer graphics and computer vision. In this work, we introduce
an approach called `LGGD' (Learned Generalized Geodesic Distances). This method
involves generating node features by learning a generalized geodesic distance
function through a training pipeline that incorporates training data, graph
topology and the node content features. The strength of this method lies in the
proven robustness of the generalized geodesic distances to noise and outliers.
Our contributions encompass improved performance in node classification tasks,
competitive results with state-of-the-art methods on real-world graph datasets,
the demonstration of the learnability of parameters within the generalized
geodesic equation on graph, and dynamic inclusion of new labels.
