  Graph convolutional neural networks (GCNNs) have been widely used in graph
learning. It has been observed that the smoothness functional on graphs can be
defined in terms of the graph Laplacian. This fact points out in the direction
of using Laplacian in deriving regularization operators on graphs and its
consequent use with spectral GCNN filter designs. In this work, we explore the
regularization properties of graph Laplacian and proposed a generalized
framework for regularized filter designs in spectral GCNNs. We found that the
filters used in many state-of-the-art GCNNs can be derived as a special case of
the framework we developed. We designed new filters that are associated with
well-defined regularization behavior and tested their performance on
semi-supervised node classification tasks. Their performance was found to be
superior to that of the other state-of-the-art techniques.
