Online Graph Dictionary Learning

Abstract

Dictionary learning is a key tool for representation learning, that explains the data as linear combination of few basic elements. Yet, this analysis is not amenable in the context of graph learning, as graphs usually belong to different metric spaces. We fill this gap by proposing a new online Graph Dictionary Learning approach, which uses the Gromov Wasserstein divergence for the data fitting term. In our work, graphs are encoded through their nodes' pairwise relations and modeled as convex combination of graph atoms, i.e. dictionary elements, estimated thanks to an online stochastic algorithm, which operates on a dataset of unregistered graphs with potentially different number of nodes. Our approach naturally extends to labeled graphs, and is completed by a novel upper bound that can be used as a fast approximation of Gromov Wasserstein in the embedding space. We provide numerical evidences showing the interest of our approach for unsupervised embedding of graph datasets and for online graph subspace estimation and tracking.

References in corpus (19)

• Adam: A Method for Stochastic Optimization
• Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift
• Natural Scales in Geographical Patterns
• Geometric deep learning: going beyond Euclidean data
• How Powerful are Graph Neural Networks?
• Soft-DTW: a Differentiable Loss Function for Time-Series
• Optimal Transport for structured data with application on graphs
• Convergence Rate of Frank-Wolfe for Non-Convex Objectives
• Concept Drift and Anomaly Detection in Graph Streams
• Understanding Attention and Generalization in Graph Neural Networks
• GOT: An Optimal Transport framework for Graph comparison
• Change Detection in Graph Streams by Learning Graph Embeddings on Constant-Curvature Manifolds
• Scalable Gromov-Wasserstein Learning for Graph Partitioning and Matching
• Distance Metric Learning using Graph Convolutional Networks: Application to Functional Brain Networks
• Fused Gromov-Wasserstein distance for structured objects: theoretical foundations and mathematical properties
• Recognizing Cuneiform Signs Using Graph Based Methods
• Nearly Optimal Robust Subspace Tracking
• Generalized Spectral Clustering via Gromov-Wasserstein Learning
• Change Point Methods on a Sequence of Graphs