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2011 NIPS NeurIPS 2011

Directed Graph Embedding: an Algorithm based on Continuous Limits of Laplacian-type Operators

Abstract

This paper considers the problem of embedding directed graphs in Euclidean space while retaining directional information. We model the observed graph as a sample from a manifold endowed with a vector field, and we design an algo- rithm that separates and recovers the features of this process: the geometry of the manifold, the data density and the vector field. The algorithm is motivated by our analysis of Laplacian-type operators and their continuous limit as generators of diffusions on a manifold. We illustrate the recovery algorithm on both artificially constructed and real data.

🌉 Interdisciplinary Bridge — Deep Learning and Machine Learning
📈 Trend Setter — Graph Neural Networks
🧭 Keyword Pioneer — directed graph embedding
🐝 Cross-Pollinator — Artificial Intelligence, Computer Science, Computer Vision, Data Science & Analytics, Deep Learning, Healthcare & Medicine, Interdisciplinary, Knowledge & Reasoning, Machine Learning, Mathematics & Optimization, Natural Language Processing, Reinforcement Learning, Speech & Audio
🐣 Hot Topic Early Bird — dimensionality reduction

Authors

Dominique C. Perrault-joncas , Marina Meila

Topics

Machine Learning > Core Methods > Embedding Learning Deep Learning > Architectures > Graph Neural Networks Knowledge & Reasoning > Reasoning > Graph Embeddings Machine Learning > Core Methods > Dimensionality Reduction Machine Learning > Core Methods > Graph Neural Networks

Keywords

dimensionality reduction manifold learning graph representation graph embedding directed graph directed graph embedding laplacian operators vector field spectral method
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