GSpect: Spectral Filtering for Cross-Scale Graph Classification

TL;DR

GSpect, an advanced spectral graph filtering model for cross-scale graph classification tasks, uses graph wavelet neural networks for the convolution layer of the model, which aggregates multi-scale messages to generate graph representations, and design a spectral-pooling layer which aggregates nodes to one node to reduce the cross-scale graphs to the same size.

Abstract

Identifying structures in common forms the basis for networked systems design and optimization. However, real structures represented by graphs are often of varying sizes, leading to the low accuracy of traditional graph classification methods. These graphs are called cross-scale graphs. To overcome this limitation, in this study, we propose GSpect, an advanced spectral graph filtering model for cross-scale graph classification tasks. Compared with other methods, we use graph wavelet neural networks for the convolution layer of the model, which aggregates multi-scale messages to generate graph representations. We design a spectral-pooling layer which aggregates nodes to one node to reduce the cross-scale graphs to the same size. We collect and construct the cross-scale benchmark data set, MSG (Multi Scale Graphs). Experiments reveal that, on open data sets, GSpect improves the performance of classification accuracy by 1.62% on average, and for a maximum of 3.33% on PROTEINS. On MSG, GSpect improves the performance of classification accuracy by 15.55% on average. GSpect fills the gap in cross-scale graph classification studies and has potential to provide assistance in application research like diagnosis of brain disease by predicting the brain network's label and developing new drugs with molecular structures learned from their counterparts in other systems.

Figures (6)

• Figure 1: An example of cross-scale graph classification
• Figure 2: The model structure of GSpect. GSpect consists of four phases. The first phase consists of the convolution layers. Each layer has F multi-scale graph wavelet convolution. The second phase is a pooling layer. This layer aggregates the nodes with similar representations in the spectrum and yields a low-order graph. The third phase is a full-connect layer for classification. the colored matrix indicate the feature vector of each node. In the second phase, nodes with similar features (depicted as the same color in the diagram) are aggregated into a single node.
• Figure 3: The distribution of of the graph size of the MSG data set
• Figure 4: Example of the MSG data set. class X-Y indicates that the graph is the Y-th example from class X.
• Figure 5: Comparison experiment between GSpect and other models on MSG.

Theorems & Definitions (4)

• Definition 1
• Proof A.1
• Proof A.2
• Definition 2