GraphLite: Compact Representation of Smooth Graphs Learned Under Log-Degree Regularization

Graph representations of data offer a rich framework for advanced signal processing applications. However, in many practical scenarios, constructing the graph is computationally demanding, and storing it can be prohibitively expensive-often requiring significantly more memory than the signal itself. This paper introduces <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">GraphLite</i>, a novel algorithm tailored for one of the good performing graph learning methods, to compactly represent the learned graph through an auxiliary vector of the same dimension as the signal. This auxiliary representation, which consists of the inverse node degree profile, arises naturally from the structure of the optimal solution and can be pre-computed and stored alongside the signal. The result is a lightweight, lossless graph representation that retains compatibility with core graph signal processing (GSP) operations. GraphLite offers a flexible and memory-efficient tool for downstream tasks in applications where both online graph construction and storage are bottlenecks.