Graph signal interpolation and extrapolation over manifold of Gaussian mixture

Abstract

Signals with an underlying irregular geometric structure are prevalent in modern applications and are often well-represented using graphs. The field of graph signal processing has emerged to accommodate such signals’ analysis, processing, and interpolation. In this paper, we address the latter, where signal samples are given only on a subset of graph nodes, and the goal is to estimate the graph signal on the remaining nodes. In addition, we consider a related extrapolation task in which new graph nodes that were not part of the original graph are added, and the goal is to estimate the graph signal on those nodes as well. We present a new approach for both the interpolation and extrapolation tasks, which is based on modeling the graph nodes as samples from a continuous manifold with a Gaussian mixture distribution and the graph signal as samples of a continuous function in a reproducing kernel Hilbert space. This model allows us to propose an interpolation and extrapolation algorithm that utilizes the closed-form expressions of the Gaussian kernel eigenfunctions. We test our algorithm on synthetic and real-world signals and compare it to existing methods. We demonstrate superior or on-par accuracy results achieved in significantly shorter run times.