Optimal Laplacian regularization for sparse spectral community detection

TL;DR

This paper formally determines an optimal Laplacian regularization for spectral clustering in sparse networks, improving upon heuristic methods and connecting to advanced spectral techniques.

Contribution

It provides a rigorous derivation of the optimal Laplacian regularization for spectral community detection in sparse graphs.

Findings

Optimal regularization improves spectral clustering performance.

The regularization parameter is theoretically justified.

Connections to state-of-the-art spectral methods are established.

Abstract

Regularization of the classical Laplacian matrices was empirically shown to improve spectral clustering in sparse networks. It was observed that small regularizations are preferable, but this point was left as a heuristic argument. In this paper we formally determine a proper regularization which is intimately related to alternative state-of-the-art spectral techniques for sparse graphs.