Performance Traits of a Newly Proposed Modularity Function for Spatial Networks: Better Assessment of Clustering for Unsupervised Learning

The “best” partition of a given network helps in revealing its naturally identifiable structures. The most modular structure is often considered as the best partition. Modularity function, is an objective measure of the quality of partitioning in a given network with that of a random graph (“Null model”), where edge between any two nodes is equally probable, are inappropriate to use for spatially embedded networks. Earlier we have proposed a new modularity function, which does not compare the network with a null model. We have analyzed a 2D and 3D granular networks which can be considered as a spatially embedded network. In all considered systems new method identifies the better partition. New function properly detects the better modular partition in 2D as well as in 3D granular assemblies as compared to the most commonly used modularity function, known as Newman modularity function, and thus is more suitable for unsupervised machine learning.