Euclidean Distances, soft and spectral Clustering on Weighted Graphs

TL;DR

This paper introduces a new class of Euclidean distances for weighted graphs that facilitate thermodynamic soft clustering, leveraging spectral clustering coordinates and higher-dimensional embeddings for improved visualization and analysis.

Contribution

It defines a novel Euclidean distance class for weighted graphs, extending spectral clustering with Schoenberg transformations for enhanced clustering and visualization.

Findings

Effective clustering of geographical flow data demonstrated

Extension of spectral clustering with higher-dimensional embeddings

Visualization benefits from the proposed distance measures

Abstract

We define a class of Euclidean distances on weighted graphs, enabling to perform thermodynamic soft graph clustering. The class can be constructed form the "raw coordinates" encountered in spectral clustering, and can be extended by means of higher-dimensional embeddings (Schoenberg transformations). Geographical flow data, properly conditioned, illustrate the procedure as well as visualization aspects.