  Convolutional Neural Networks (CNNs) have enabled major advances in image
classification through convolution and pooling. In particular, image pooling
transforms a connected discrete lattice into a reduced lattice with the same
connectivity and allows reduction functions to consider all pixels in an image.
However, there is no pooling that satisfies these properties for graphs. In
fact, traditional graph pooling methods suffer from at least one of the
following drawbacks: Graph disconnection or overconnection, low decimation
ratio, and deletion of large parts of graphs. In this paper, we present three
pooling methods based on the notion of maximal independent sets that avoid
these pitfalls. Our experimental results confirm the relevance of maximal
independent set constraints for graph pooling.
