Due to high utility in many applications, from social networks to blockchain to power grids, deep learning on non-Euclidean objects such as graphs and manifolds continues to gain an ever increasing interest. Most currently available techniques are based on the idea of performing a convolution operation in the spectral domain with a suitably chosen nonlinear trainable filter and then approximating the filter with finite order polynomials. However, such polynomial approximation approaches tend to be both non-robust to changes in the graph structure and to capture primarily the global graph topology. In this paper we propose a new Fractional Generalized Graph Convolutional Networks (FGCN) method for semisupervised learning, which casts the Lévy Flights into random walks on graphs and, as a result, allows to more accurately account for the intrinsic graph topology and to substantially improve classification performance, especially for heterogeneous graphs.
This paper proposes a fractional graph convolutional networks for semi-supervised learning. The proposed method used a classification function of a fractional graph semi-supervised learning (GSSL) [De Nigris et al., 2017] as a graph filter. In addition, the authors adopt a parallel system and weighted combination of max and average pool. Experimental results show that the proposed method (FGCN) shows the best accuracy compared to other recent graph-based neural networks for all datasets except one.
The key approach of the proposed method is to apply a classification function (equation (3)) obtained by solving a GSSL problem to graph convolutional networks. However, this idea is too incremental and applying the classification function to graph filter is very trivial. This works also combines the fractional GSSL with a parallel system and weighted pool. But, it is not clear which contribution actually improves the results. Moreover, the intuition of the fractional approach is not clear too, e.g., how the optimization (equation (2)) is derived?, and some explanations are unnatural to demonstrate the methodology, e.g., equation (4). For these reasons, this paper is under the bar of acceptance.
Main concerns:
1. What is the intuition of the optimization of GSSL? How is it obtained? And among all fractional methods (e.g., SL, NL, and PR), which one doe achieve the best performance?
2. The FGS filter in equation (7) is the sum of infinite terms. However, in practical, it is impossible to compute the infinite terms. Does this approximate the sum of finite terms? If does, what is the number of truncation?
3. The authors mention that they establish a theoretical guarantee of the parallel system. But, I could not find any theoretical results. It would be better to include the analysis in the paper.
Minor concerns:
1. In page 3, please edit “forulation” -> “formulation”
2. In equation (8), I think “X+\alpha \tilde{L} X” should change to “\tilde{L} X”