Root Laplacian Eigenmaps with their application in spectral embedding

TL;DR

This paper explores the root Laplacian operator, its mathematical properties, and potential applications in spectral clustering and graph signal processing within geometric deep learning.

Contribution

It introduces the concept of the root Laplacian in graph theory and discusses its applications in spectral embedding and related fields.

Findings

Potential applications in spectral clustering

Relevance to graph signal processing

Connection to geometric deep learning

Abstract

The root laplacian operator or the square root of Laplacian which can be obtained in complete Riemannian manifolds in the Gromov sense has an analog in graph theory as a square root of graph-Laplacian. Some potential applications have been shown in geometric deep learning (spectral clustering) and graph signal processing.