Trend Filtering on Graphs.

We introduce a family of adaptive estimators on graphs, based on penalizing the l(1) norm of discrete graph differences. This generalizes the idea of trend filtering [11, 26], used for univariate nonparametric regression, to graphs. Analogous to the univariate case, graph trend filtering exhibits a level of local adaptivity unmatched by the usual l(2)-based graph smoothers. It is also defined by a convex minimization problem that is readily solved (e.g., by fast ADMM or Newton algorithms). We demonstrate the merits of graph trend filtering through examples and theory.