Learning Graphs With Monotone Topology Properties and Multiple Connected Components - 2018


Recent papers have formulated the problem of learning graphs from information as an inverse covariance estimation downside with graph Laplacian constraints. While such problems are convex, existing methods cannot guarantee that solutions can have specific graph topology properties (e.g., being a tree), that are desirable for a few applications. The matter of learning a graph with topology properties is generally non-convex. During this Project, we propose an approach to unravel these problems by decomposing them into 2 sub-problems for which economical solutions are known. Specifically, a graph topology inference (GTI) step is used to pick a feasible graph topology. Then, a graph weight estimation (GWE) step is performed by solving a generalized graph Laplacian estimation drawback, where edges are constrained by the topology found within the GTI step. Our main result's a bound on the error of the GWE step as a operate of the error within the GTI step. This error sure indicates that the GTI step ought to be solved using an algorithm that approximates the info similarity matrix by another matrix whose entries are thresholded to zero to own the specified type of graph topology. The GTI stage can leverage existing ways, that are usually primarily based on minimizing the entire weight of removed edges. Since the GWE stage is an inverse covariance estimation drawback with linear constraints, it can be solved using existing convex optimization ways. We demonstrate that our approach will achieve smart results for each artificial and texture image data.

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