This post summarizes the NIPS 2016 paper by Defferrard et al on " Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering ". Convolutional Neural Networks have accomplished many breakthroughs, ranging from a classification of a million images of ImageNet to very complex tasks like object tracking in surveillance videos. These advancements are not restricted to image data. The CNNs (and, in general, deep learning concepts) have been able to achieve state-of-the-art results even on text and speech applications. CNNs are proved to be very powerful tool in solving many problems from images, text and speech domain. If that is the case then the question that we want to ask here is, can we use CNNs to solve problems on graphs as well. If we take a closer look at the data domain that we were dealing with, we realize that this data has specific structure, e.g. images are nothing but the 2-D grid of pixels, the text is a stream of words and can be t
This post summarizes the PATCHY-SAN algorithm proposed by Niepert et al in their ICML 2016 paper " Learning Convolutional Neural Networks for Graphs " In the literature, the convolution operation on graphs is defined in 3 domains: spectral domain [ Defferrard et al , Kipf et al ], spatial domain [ Masci et al , Boscaini et al ] and embedding domain [ Maron et al ]. The method proposed by Niepert et al in "Learning Convolutional Neural Networks for Graphs" falls into the category of spatial domain algorithm. The broad aim of the paper is to learn a function over a bunch of graphs that will give us a general representation of them. These representations can then be used for any task such graph classification. Challenges in applying convolution directly on graphs: There are two main problems that needs to be addressed before we could apply convolution on graphs. Challenge 1 : Images can be thought of as a regular graph, where each pixel is denoted by a