Semi-supervised Learning in Network-Structured Data via Total Variation Minimization

Abstract

We propose and analyze a method for semi-supervised learning from partially-labeled network-structured data. Our approach is based on a graph signal recovery interpretation under a clustering hypothesis that labels of data points belonging to the same well-connected subset (cluster) are similar valued. This lends naturally to learning the labels by total variation (TV) minimization, which we solve by applying a recently proposed primal-dual method for non-smooth convex optimization. The resulting algorithm allows for a highly scalable implementation using message passing over the underlying empirical graph, which renders the algorithm suitable for big data applications. By applying tools of compressed sensing, we derive a sufficient condition on the underlying network structure such that TV minimization recovers clusters in the empirical graph of the data. In particular, we show that the proposed primal-dual method amounts to maximizing network flows over the empirical graph of the dataset. Moreover, the learning accuracy of the proposed algorithm is linked to the set of network flows between data points having known labels. The effectiveness and scalability of our approach is verified by numerical experiments.

References in corpus (9)

• Benchmark graphs for testing community detection algorithms
• NESTA: A Fast and Accurate First-order Method for Sparse Recovery
• Efficient Sampling Set Selection for Bandlimited Graph Signals Using Graph Spectral Proxies
• Signal Recovery on Graphs: Variation Minimization
• Network Lasso: Clustering and Optimization in Large Graphs
• Optimal rates for total variation denoising
• Asymptotic behavior of ${\ell }_p$-based Laplacian regularization in semi-supervised learning
• Algorithms for Lipschitz Learning on Graphs
• Sparse Recovery over Graph Incidence Matrices

Cited by in corpus (5)

• Graph Signal Processing: Dualizing GSP Sampling in the Vertex and Spectral Domains
• Local Graph Clustering with Network Lasso
• Compressed Regression over Adaptive Networks
• Flow-based Algorithms for Improving Clusters: A Unifying Framework, Software, and Performance
• Statistical Analysis of Multi-Relational Network Recovery