  Deep Graph Neural Networks (GNNs) are useful models for graph classification
and graph-based regression tasks. In these tasks, graph pooling is a critical
ingredient by which GNNs adapt to input graphs of varying size and structure.
We propose a new graph pooling operation based on compressive Haar transforms
-- HaarPooling. HaarPooling implements a cascade of pooling operations; it is
computed by following a sequence of clusterings of the input graph. A
HaarPooling layer transforms a given input graph to an output graph with a
smaller node number and the same feature dimension; the compressive Haar
transform filters out fine detail information in the Haar wavelet domain. In
this way, all the HaarPooling layers together synthesize the features of any
given input graph into a feature vector of uniform size. Such transforms
provide a sparse characterization of the data and preserve the structure
information of the input graph. GNNs implemented with standard graph
convolution layers and HaarPooling layers achieve state of the art performance
on diverse graph classification and regression problems.
