Department of Mathematics, Faculty of Science, Muğla Sıtkı Koçman University, 48000 Muğla, Turkey.
Department of Business, Babeş-Bolyai University, 7 Horea Street, 400174 Cluj-Napoca, Romania.
Sensors (Basel). 2023 Feb 21;23(5):2398. doi: 10.3390/s23052398.
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.
在离散几何数据的结构分析中，图核函数具有出色的性能记录。使用图核函数有两个显著的优势。首先，图核函数能够通过在高维空间中描述图的属性来保留图的拓扑结构。其次，图核函数允许将机器学习方法应用于快速演化为图的向量数据。本文提出了一种用于确定点云数据结构相似性的核函数，该函数对于许多应用至关重要。该函数由反映点云底层离散几何的图中测地线路径分布的接近程度确定。这项研究展示了这种独特核函数在相似性度量和点云分类方面的效率。
