Dan Sun

Xue Liu, Dan Sun, Xiaobo Cao et al.

Graph embedding provides a feasible methodology to conduct pattern classification for graph-structured data by mapping each data into the vectorial space. Various pioneering works are essentially coding method that concentrates on a vectorial representation about the inner properties of a graph in terms of the topological constitution, node attributions, link relations, etc. However, the classification for each targeted data is a qualitative issue based on understanding the overall discrepancies within the dataset scale. From the statistical point of view, these discrepancies manifest a metric distribution over the dataset scale if the distance metric is adopted to measure the pairwise similarity or dissimilarity. Therefore, we present a novel embedding strategy named $\mathbf{MetricDistribution2vec}$ to extract such distribution characteristics into the vectorial representation for each data. We demonstrate the application and effectiveness of our representation method in the supervised prediction tasks on extensive real-world structural graph datasets. The results have gained some unexpected increases compared with a surge of baselines on all the datasets, even if we take the lightweight models as classifiers. Moreover, the proposed methods also conducted experiments in Few-Shot classification scenarios, and the results still show attractive discrimination in rare training samples based inference.

Xue Liu, Dan Sun, Wei Wei

The Graph Convolutional Networks (GCN) proposed by Kipf and Welling is an effective model for semi-supervised learning, but faces the obstacle of over-smoothing, which will weaken the representation ability of GCN. Recently some works are proposed to tackle above limitation by randomly perturbing graph topology or feature matrix to generate data augmentations as input for training. However, these operations inevitably do damage to the integrity of information structures and have to sacrifice the smoothness of feature manifold. In this paper, we first introduce a novel graph entropy definition as a measure to quantitatively evaluate the smoothness of a data manifold and then point out that this graph entropy is controlled by triangle motif-based information structures. Considering the preservation of graph entropy, we propose an effective strategy to generate randomly perturbed training data but maintain both graph topology and graph entropy. Extensive experiments have been conducted on real-world datasets and the results verify the effectiveness of our proposed method in improving semi-supervised node classification accuracy compared with a surge of baselines. Beyond that, our proposed approach could significantly enhance the robustness of training process for GCN.