In the structural analysis of discrete geometric data, graph kernels have a great track record of performance. Using graph kernel functions provides two significant advantages. First, a graph kernel is capable of preserving the graph's topological structures by describing graph properties in a high-dimensional space. Second, graph kernels allow the application of machine learning methods to vector data that are rapidly evolving into graphs. In this paper, the unique kernel function for similarity determination procedures of point cloud data structures, which are crucial for several applications, is formulated. This function is determined by the proximity of the geodesic route distributions in graphs reflecting the discrete geometry underlying the point cloud. This research demonstrates the efficiency of this unique kernel for similarity measures and the categorization of point clouds.
Keywords: Kullback–Leibler information; Wasserstein distance; point cloud processing; simplicial complex.