Maximal Independent Vertex Set applied to Graph Pooling

TL;DR

This paper introduces MIVSPool, a novel graph pooling method that preserves all vertex information by selecting a Maximal Independent Vertex Set, improving graph classification accuracy without losing data.

Contribution

The paper proposes a new graph pooling technique using Maximal Independent Vertex Sets that maintains all vertex information and avoids artificial graph density increase.

Findings

Improved accuracy on standard graph classification datasets

Preserves all vertex information during pooling

Avoids artificial increase in graph density

Abstract

Convolutional neural networks (CNN) have enabled major advances in image classification through convolution and pooling. In particular, image pooling transforms a connected discrete grid into a reduced grid with the same connectivity and allows reduction functions to take into account all the pixels of an image. However, a pooling satisfying such properties does not exist for graphs. Indeed, some methods are based on a vertex selection step which induces an important loss of information. Other methods learn a fuzzy clustering of vertex sets which induces almost complete reduced graphs. We propose to overcome both problems using a new pooling method, named MIVSPool. This method is based on a selection of vertices called surviving vertices using a Maximal Independent Vertex Set (MIVS) and an assignment of the remaining vertices to the survivors. Consequently, our method does not discard any vertex information nor artificially increase the density of the graph. Experimental results show an increase in accuracy for graph classification on various standard datasets.