Abstract
Feature extraction and dimension reduction for networks is critical in a wide variety of domains. Efficiently and accurately learning features for multiple graphs has important applications in statistical inference on graphs. We propose a method to jointly embed multiple undirected graphs. Given a set of graphs, the joint embedding method identifies a linear subspace spanned by rank one symmetric matrices and projects adjacency matrices of graphs into this subspace. The projection coefficients can be treated as features of the graphs, while the embedding components can represent vertex features. We also propose a random graph model for multiple graphs that generalizes other classical models for graphs. We show through theory and numerical experiments that under the model, the joint embedding method produces estimates of parameters with small errors. Via simulation experiments, we demonstrate that the joint embedding method produces features which lead to state of the art performance in classifying graphs. Applying the joint embedding method to human brain graphs, we find it extracts interpretable features with good prediction accuracy in different tasks.
Highlights
I N many problems arising in science and engineering, graphs arise naturally as data structure to capture complex relationships between a set of objects
The 1-dimensional joint embedding is well defined in this case, that is λi and h1 defined in Equation 1 is guaranteed to exist
We proposed a Multiple Random Eigen Graphs model
Summary
I N many problems arising in science and engineering, graphs arise naturally as data structure to capture complex relationships between a set of objects. Graphs have been used in various application domains as diverse as social networks [1], internet mapping [2], brain connectomics [3], political voting networks [4], and many others. The graphs are naturally high dimensional objects with complicated topological structure, which makes graph clustering and classification a challenge to traditional machine learning algorithms. Feature extraction and dimension reduction techniques are helpful in the applications of learning graph data. We demonstrate through theory and experiments that the joint embedding algorithm produces features which lead to state of the art performance for subsequent inference tasks on graphs
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More From: IEEE Transactions on Pattern Analysis and Machine Intelligence
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