Vector-Valued Graph Trend Filtering with Non-Convex Penalties
This work addresses denoising and analysis of complex graph data for applications like event detection and classification, but it is incremental as it builds on existing graph trend filtering frameworks.
The paper tackles denoising piecewise smooth vector-valued graph signals with inhomogeneous smoothness by extending graph trend filtering with non-convex penalties, showing superior recovery performance over convex methods and establishing statistical error rates for generic graphs.
This work studies the denoising of piecewise smooth graph signals that exhibit inhomogeneous levels of smoothness over a graph, where the value at each node can be vector-valued. We extend the graph trend filtering framework to denoising vector-valued graph signals with a family of non-convex regularizers, which exhibit superior recovery performance over existing convex regularizers. Using an oracle inequality, we establish the statistical error rates of first-order stationary points of the proposed non-convex method for generic graphs. Furthermore, we present an ADMM-based algorithm to solve the proposed method and establish its convergence. Numerical experiments are conducted on both synthetic and real-world data for denoising, support recovery, event detection, and semi-supervised classification.