A Markov Variation Approach to Smooth Graph Signal Interpolation

TL;DR

This paper introduces a probabilistic smoothness measure called Markov variation for graph signals, developing an efficient interpolation method that outperforms existing techniques on real datasets with faster computation.

Contribution

It proposes a novel Markov variation measure for graph signal smoothness and an efficient Nyström extension-based interpolation framework for large graphs.

Findings

Outperforms state-of-the-art graph signal interpolation methods

Achieves significant computational speedup with minimal accuracy loss

Demonstrated on MNIST and temperature datasets

Abstract

In this paper we present the Markov variation, a smoothness measure which offers a probabilistic interpretation of graph signal smoothness. This measure is then used to develop an optimization framework for graph signal interpolation. Our approach is based on diffusion embedding vectors and the connection between diffusion maps and signal processing on graphs. As diffusion embedding vectors may be expensive to compute for large graphs, we present a computationally efficient method, based on the Nystr\"{o}m extension, for interpolation of signals over a graph. We demonstrate our approach on the MNIST dataset and a dataset of daily average temperatures around the US. We show that our method outperforms state of the art graph signal interpolation techniques on both datasets, and that our computationally efficient reconstruction achieves slightly reduced accuracy with a large computational speedup.