DeepAI AI Chat
Log In Sign Up

On spectral embedding performance and elucidating network structure in stochastic block model graphs

by   Joshua Cape, et al.

Statistical inference on graphs often proceeds via spectral methods involving low-dimensional embeddings of matrix-valued graph representations, such as the graph Laplacian or adjacency matrix. In this paper, we analyze the asymptotic information-theoretic relative performance of Laplacian spectral embedding and adjacency spectral embedding for block assignment recovery in stochastic block model graphs by way of Chernoff information. We investigate the relationship between spectral embedding performance and underlying network structure (e.g. homogeneity, affinity, core-periphery, (un)balancedness) via a comprehensive treatment of the two-block stochastic block model and the class of K-block models exhibiting homogeneous balanced affinity structure. Our findings support the claim that, for a particular notion of sparsity, loosely speaking, "Laplacian spectral embedding favors relatively sparse graphs, whereas adjacency spectral embedding favors not-too-sparse graphs." We also provide evidence in support of the claim that "adjacency spectral embedding favors core-periphery network structure."


page 18

page 20

page 21

page 23


Statistical inference on random dot product graphs: a survey

The random dot product graph (RDPG) is an independent-edge random graph ...

Decentralized core-periphery structure in social networks accelerates cultural innovation in agent-based model

Previous investigations into creative and innovation networks have sugge...

Weighted Spectral Embedding of Graphs

We present a novel spectral embedding of graphs that incorporates weight...

Limit theorems for out-of-sample extensions of the adjacency and Laplacian spectral embeddings

Graph embeddings, a class of dimensionality reduction techniques designe...

On a 'Two Truths' Phenomenon in Spectral Graph Clustering

Clustering is concerned with coherently grouping observations without an...

Spectral embedding and the latent geometry of multipartite networks

Spectral embedding finds vector representations of the nodes of a networ...

Beyond the adjacency matrix: random line graphs and inference for networks with edge attributes

Any modern network inference paradigm must incorporate multiple aspects ...