Learning Graphs From Data: A Signal Representation Perspective

Abstract

The construction of a meaningful graph topology plays a crucial role in the effective representation, processing, analysis and visualization of structured data. When a natural choice of the graph is not readily available from the data sets, it is thus desirable to infer or learn a graph topology from the data. In this tutorial overview, we survey solutions to the problem of graph learning, including classical viewpoints from statistics and physics, and more recent approaches that adopt a graph signal processing (GSP) perspective. We further emphasize the conceptual similarities and differences between classical and GSP-based graph inference methods, and highlight the potential advantage of the latter in a number of theoretical and practical scenarios. We conclude with several open issues and challenges that are keys to the design of future signal processing and machine learning algorithms for learning graphs from data.

Recursive Prediction of Graph Signals With Incoming Nodes

“…This includes a wealth of techniques from harmonic and filterbank analysis [5,6,7,8], sampling [9,10,11], statistical analysis [12], non-parametric analysis [2,13,14], prediction and recovery [15,16] to the more recent graph neural networks [17]. The second group deals with the problem of graph estimation or discovery where the graph signals are used to arrive at an estimate of the graph or the connections among the nodes [18,19,20]. Recursive approaches have been considered in the context of distributed recursive least squares by Mateo et al [21,22].…”

Time-varying Graph Learning Based on Sparseness of Temporal Variation

“…Several approaches address graph learning problem, and two overview papers about graph learning have been published recently [14], [15]. Among the techniques for learning timevarying graphs, the Kalofolias et al method, where constraints are introduced so that the edge weights change smoothly over time, is close to ours [33].…”

Fast Graph Convolutional Recurrent Neural Networks

“…The stability of the gradient depends on the largest eigenvalue of (8). If its value is sufficiently small, i.e., < 1 the gradient will shrink exponentially.…”