GRAPH AUTO-ENCODER FOR GRAPH SIGNAL DENOISING Tien Huu Do, Duc Minh Nguyen, Nikos Deligiannis Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Brussels, Belgium imec, Kapeldreef 75, B-3001 Leuven, Belgium ABSTRACT Signal denoising is an important problem with a vast litera- ture. Recently, signal denoising on graphs has received a lot of attention due to the increasing use of graph-structured sig- nals. However, well-etablished signal denoising methods do not generalize to graph signals with irregular structures, while existing graph denoising methods do not capture well the ab- stract representations inherent in the signals. To bridge this gap, we propose to use graph convolutional neural network with a Kron-reduction-based pooling operator for denoising on graphs. The proposed model can effectively capture the ir- regular data structure and learn the underlying representations in the signals, leading to improved performance over existing methods in experiments involving real-world traffic signals. Index Terms— graph signal denoising, graph auto- encoders, graph neural network, geometric deep learning. 1. INTRODUCTION Denoising refers to the task of reconstructing signals from noisy observations. As noisy signals arise in many contexts due to the nature of the data collection processes, especially in the current data deluge era when the volume of data is grow- ing exponentially over the years, signal denoising has become a highly meaningful research problem. Although signal de- noising is a classical research topic, existing work focuses mainly on regular-structured signals, such as time series, im- ages and audio, while ignoring irregular-structured signals. Irregular-structured signals are normally represented in the form of graphs. Users’ networks on social media platforms, location-based measurements in traffic monitoring systems or in air quality monitoring applications are all examples of such type of signals. In response to this, this work focuses on the task of signal denoising on graphs. Traditional denoising methods often rely on smooth- ing operators [1], regularization techniques [2] or multi- resolution analysis [3] to remove the noise from the true signal. Recently, like in many application domains of signal processing and machine learning, deep-learning-based meth- ods have been used widely for denoising. For example, a deep auto-encoder was proposed to learn sparse hidden represen- tations and reconstruct the noise-free version of the signals, which lead to high performance on image data [4]. In [5], an autoregressive generative model, which was equipped with causal, dilated convolutions and skip connections, was pro- posed for the task of speech denoising. Despite achieving high performance, existing denoising deep-learning-based methods only operate on signals in the Euclidean domain, and do not generalize to graph signals with irregular struc- tures [6]. A considerable research effort has been spent on graph signal denoising [7, 8, 9]. In [7, 8], the task was formu- lated as an optimization problem which was then solved in closed-form. In [9], a method for denoising graph signals was proposed, which relies on a trilateral filter defined in the graph spectral domain. Despite being able to directly model the irregular structures of the signals, these methods do not capture well the abstract representations of the signals, which has been shown useful for denoising with deep neural net- works [4, 5]. Motivated by this, we aim at a method for graph signal denoising that (i) effectively models the irregular data struc- ture and (ii) is capable of capturing the underlying abstract representation of the signals. To this end, we leverage the recent advances in geometric deep learning (which refers to the generalization of deep neural networks to non-Euclidean domains [6]) for the task of signal denoising on graphs. Ge- ometric deep models are often referred to as graph neural networks (GNNs), which have been successfully applied to a wide range of problems, such as graph classification [10], node classification [11] and graph clustering [12]. To sum- marize, our contributions in this work are two-fold: • We propose to use a graph convolutional neural net- work (GCN) [11]—a well-established GNN architecture— for denoising signals on graphs. To the best of our knowledge, this is the first work to use GNNs for de- noising. In addition, we propose to integrate graph Kron-reduction-based pooling and unpooling layers, which lead to consistent performance improvements over the original GCN model. • We evaluate the proposed model on a real-world traffic dataset. The result shows the good performance of our model in terms of the quality of the denoised signals.