Learning graph from graph signals: An approach based on sensitivity analysis over a deep learning framework

Abstract

Utilizing a meaningful graph plays an essential part in the performance of graph-based algorithms. However, a ground-truth graph representing the relationships between data points is not readily available in many applications. This paper proposes a graph learning method based on sensitivity analysis over a deep learning framework called GL-SADL. The proposed method is composed of two steps. First, it estimates the signal value for each vertex using the signal values corresponding to the other vertices with a Deep Neural Network (DNN) block. Then a sensitivity analysis approach is applied to each DNN block to determine how the input signal values influence the DNN’s response. This procedure leads us to the underlying graph structure. The utilization of DNNs allows us to take advantage of the non-linearity characteristics of neural networks in modeling the observed graph signals. In addition, since the DNNs are considered as general approximators, there is no need to make any prior assumptions about the distribution of the observed graph signals. Experiments with synthetic and real-world datasets demonstrate that the proposed method can infer meaningful graph structures from observed graph signals.