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Title: | Gradient-based spectral embeddings of Random Dot Product Graphs. |
Authors: | Fiori, Marcelo Marenco, Bernardo Larroca, Federico Bermolen, Paola Mateos, Gonzalo |
Type: | Artículo |
Keywords: | Graph representation learning, Gradient descent, Manifold optimization, Random dot product graphs, Optimization, Information processing, Matrix decomposition, Manifolds, Representation learning, Data models, Scalability |
Issue Date: | 2024 |
Abstract: | The Random Dot Product Graph (RDPG) is a generative model for relational data, where nodes are represented via latent vectors in low-dimensional Euclidean space. RDPGs crucially postulate that edge formation probabilities are given by the dot product of the corresponding latent positions. Accordingly, the embedding task of estimating these vectors from an observed graph is typically posed as a low-rank matrix factorization problem. The workhorse Adjacency Spectral Embedding (ASE) enjoys solid statistical properties, but it is formally solving a surrogate problem and can be computationally intensive. In this paper, we bring to bear recent advances in non-convex optimization and demonstrate their impact to RDPG inference. We advocate first-order gradient descent methods to better solve the embedding problem, and to organically accommodate broader network embedding applications of practical relevance. Notably, we argue that RDPG embeddings of directed graphs loose interpretability unless the factor matrices are constrained to have orthogonal columns. We thus develop a novel feasible optimization method in the resulting manifold. The effectiveness of the graph representation learning framework is demonstrated on reproducible experiments with both synthetic and real network data. Our open-source algorithm implementations are scalable, and unlike the ASE they are robust to missing edge data and can track slowly-varying latent positions from streaming graphs. |
IN: | IEEE Transactions on Signal and Information Processing over Networks, vol. 10, 2024, pp. 1-16. |
Sponsors: | Este trabajo cuenta con el apoyo parcial de CSIC (proyecto de I+D 22520220100076UD) y de los premios NSF CCF-1750428, CCF-1934962. |
Citation: | Fiori, M., Marenco, B., Larroca, F. y otros. "Gradient-based spectral embeddings of Random Dot Product Graphs". IEEE Transactions on Signal and Information Processing over Networks. [en línea]. 2024, vol. 10, pp. 1-16. |
Academic department: | Telecomunicaciones |
Investigation group: | Análisis de Redes, Tráficos y Estadísticas de Servicios (ARTES) |
Appears in Collections: | Publicaciones académicas y científicas - Instituto de Ingeniería Eléctrica |
Files in This Item:
File | Description | Size | Format | ||
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FMLBM24.pdf | Versión final | 1,03 MB | Adobe PDF | View/Open |
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