On spectral embedding performance and elucidating network structure in stochastic blockmodel graphs
Bibliographic Data
| ID | 6161473 |
|---|---|
| Authors | Joshua Cape (0000-0002-1471-1650), Minh Tang (0000-0003-1420-7187), Carey E Priebe (0000-0002-0139-7201) |
| Year | 2019 |
| Volume | 7 |
| Issue | 3 |
| Pages | 269-291 |
| Publication date | 2019-09-01 |
| Open Access | Yes |
| Type | PREPRINT |
| Venue | Network Science (JOURNAL) |
| Journal identifiers | ISSN: 2050-1250 • E-ISSN: 2050-1242 |
| Publisher | Cambridge University Press (PUBLISHER • US) |
| DOI | 10.1017/nws.2019.23 |
| OpenAlex | W2885573525 |
| Language | EN |
| Citations received | 1 |
| References cited | 29 |
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 blockmodel graphs by way of Chernoff information. We investigate the relationship between spectral embedding performance and underlying network structure (e.g., homogeneity, affinity, core-periphery, and (un)balancedness) via a comprehensive treatment of the two-block stochastic blockmodel and the class of K -blockmodels 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
Adjacency list · Adjacency matrix · Block (permutation group theory · Combinatorics · Embedding · Graph · Inference · Stochastic block model · Complex Network Analysis Techniques · Computer Science · Graph theory and applications · Markov Chains and Monte Carlo Methods · Mathematics · Artificial Intelligence · Theoretical Computer Science
| Citations per year | 0.33 |
|---|---|
| Citation span | 2023 - 2023 (1) |
| Highly cited | No |