Construction of Networks by Associating with Submanifolds of Almost Hermitian Manifolds

Abstract

The idea that data lies in a non-linear space has brought up the concept of manifold learning as a part of machine learning and such notion is one of the most important research fields of today. The main idea here is to design the data as a submanifold model embedded in a high-dimensional manifold. On the other hand, graph theory is one of the most important research areas of applied mathematics and computer science. As a result, many researchers investigate new methods for machine learning on graphs. From the above information, it is seen that the theory of submanifolds and graph theory have become two important concepts in machine learning and nowadays, the geometric deep learning research area using these two concepts has emerged. By combining these two fields, this article aims to present the relationships between submanifolds of complex manifolds with the help of graphs. In this paper, we build some directed networks by identifying with submanifolds of almost Hermitian manifolds. Moreover, we give some results and relations among holomorphic submanifolds, totally real submanifolds, CR-submanifolds, slant submanifolds, semi-slant submanifolds, hemi-slant submanifolds, and bi-slant submanifolds in almost Hermitian manifolds in terms of graph theory.1. D 1 is a bipartite digraph as well as a complete bipartite digraph. 2. D 1 has a perfect matching.