Graph Embedding for Community Detection and Random Walks
Date:
I gave a talk at the Graduate Student Seminar at IU Math Department.
Title: Graph Embedding for Community Detection and Random Walks
Abstract: In this talk, we will cover the applications of network embedding in network data clustering. To achieve data clustering on networks, we may utilize network embedding algorithms to transform network nodes into vector representations in Euclidean spaces. Employing the k-means clustering technique on vectors in Euclidean spaces, we can successfully identify cluster structures within perturbed networks after removing nodes. Specifically, we compare newly obtained cluster structures and the original cluster structures using element-centric similarity. Our findings offer valuable insights to the realm of network data analysis and provide practical guidance for recovering cluster structures under network perturbations. On the other hand, using spectral embedding technique, we give sharp bounds on return probabilities of simple random walk on networks. Bounds on eigenvalues of random walk transition matrices will also be given. We will mention Cheeger-type inequalities, which connects eigenvalues and network structure.