Manifold Clustering in the setting of Generalized Random Dot Product Graphs

It has been shown that network models with community structure, such as the stochastic block model and its generalizations, can be defined as generalized random dot product graphs with various community-wise structures. As an example, the stochastic block model is a generalized random dot product graph in which the communities are represented by point masses in the latent space. Based on this connection, we define the manifold block model as a generalized random dot product graph in which the communities are represented by manifolds in the latent space. The manifold block model is motivated by networks observed in real data. This leads to the K-curves clustering algorithm for community detection in this setting. We derive asymptotic properties for a semi-supervised version of this algorithm and demonstrate them via simulation.

network analysis

spectral clustering

community detection

random dot product graph

manifold learning

clustering 

Mid-Level

Machine Learning

Symposium on Data Science and Statistics (SDSS) 2023