Spectral embedding for dynamic networks with stability guarantees
Authors: Ian Gallagher, Andrew Jones, Patrick Rubin-Delanchy
NeurIPS 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Section 2 gives a pedagogical example demonstrating the cross-sectional and longitudinal stability of UASE in a two-step dynamic stochastic block model, while highlighting the instability of omnibus and independent spectral embedding. In Section 3, we prove a central limit theorem for UASE under a dynamic latent position model, and demonstrate that the distribution satisfies both stability conditions. In Section 4, we review the stability of other dynamic network embedding procedures. Section 5 presents an example of UASE applied to a dynamic network of social interactions in a French primary school, with a dynamic community detection example given in the main text and a further classification example provided in the Appendix. |
| Researcher Affiliation | Academia | Ian Gallagher University of Bristol, UK ian.gallagher@bristol.ac.uk Andrew Jones University of Bristol, UK andrew.jones@bristol.ac.uk Patrick Rubin-Delanchy University of Bristol, UK patrick.rubin-delanchy@bristol.ac.uk |
| Pseudocode | Yes | Algorithm 1 Unfolded adjacency spectral embedding for dynamic networks input symmetric adjacency matrices A(1), . . . , A(T ) 2 {0, 1}n n, embedding dimension d 1: Form the matrix A = (A(1)| |A(T )) 2 {0, 1}n T n (column concatenation) 2: Compute the truncated singular value decomposition UA AV> A of A, where A contains the d largest singular values of A, and UA, VA the corresponding left and right singular vectors 3: Compute the right embedding ˆY = VA 1/2 A 2 RT n d and create sub-embeddings ˆY(t) 2 Rn d where ˆY = ( ˆY(1); . . . ; ˆY(T )) (row concatenation) return node embeddings for each time period ˆY(1), . . . , ˆY(T ) |
| Open Source Code | No | The paper does not explicitly state that the source code for the described methodology is available, nor does it provide a link to a code repository. |
| Open Datasets | Yes | The Lyon primary school data set shows the social interactions at a French primary school over two days in October 2009 [44]. ... The data are available for download from the Network Repository website1 [34]. 1https://networkrepository.com |
| Dataset Splits | No | The paper mentions simulating a dynamic network and using the Lyon primary school data set, but it does not specify any explicit training, validation, or test dataset splits for reproduction. |
| Hardware Specification | Yes | taking approximately five seconds on a 2017 Mac Book Pro |
| Software Dependencies | No | The paper does not provide specific software dependencies with version numbers (e.g., 'Python 3.8, PyTorch 1.9'). |
| Experiment Setup | Yes | Given the unfolded adjacency matrix A = (A(1)| |A(20)), an estimated embedding dimension ˆd = 10 was obtained using profile likelihood [55] and we construct the embeddings ˆY(1), . . . , ˆY(20) 2 Rn 10, taking approximately five seconds on a 2017 Mac Book Pro. |