Constant Approximation for Normalized Modularity and Associations Clustering
Data Structures and Algorithms
2023-01-02 v1 Machine Learning
Social and Information Networks
Abstract
We study the problem of graph clustering under a broad class of objectives in which the quality of a cluster is defined based on the ratio between the number of edges in the cluster, and the total weight of vertices in the cluster. We show that our definition is closely related to popular clustering measures, namely normalized associations, which is a dual of the normalized cut objective, and normalized modularity. We give a linear time constant-approximate algorithm for our objective, which implies the first constant-factor approximation algorithms for normalized modularity and normalized associations.
Keywords
Cite
@article{arxiv.2212.14334,
title = {Constant Approximation for Normalized Modularity and Associations Clustering},
author = {Jakub Łącki and Vahab Mirrokni and Christian Sohler},
journal= {arXiv preprint arXiv:2212.14334},
year = {2023}
}