Abstract:
The success behind Deep Learning have mostly relied on Convolutional Neural
Network. Convolutional Neural Networks became popular because of their e -
cient ability to exploit signi cant statistical properties of images, audio and video
data which allows depicting long range interactions in the form of smaller, localized
interactions. In Machine Learning, localized feature in the regular domain
boosted the use of Convolutional Neural Network, with great advancement in the
image processing and classi cation. But there exist some domains such as social
networks, bio-informatics data which lack few or all of these fundamental statistical
properties and considered as the high-dimensional irregular domain. Being
non-trivial in the design and convolution of a kernel lter there arises an issue
with the use of Convolution Neural Network within irregular spatial domain. Solution
to this problem can be in two direction, where one is to represent these high
dimensional irregular domains using graph and then use graph signal processing
methods and theorems to execute convolution on graph structure of irregular domain
to extract features maps to learnt lters. So, graph convolution and pooling
operators like those for regular domain can be a solution to this problem. Other
solution to this problem can go in a direction where by calculating gradients on the
data input and spectral lter, can achieve deep learning of a problem of irregular
spatial domain. Here we will focus on general query of how to build deep networks
on non-Euclidean domains in context of spectral theory over graphs with
small complexity in its learning. Importantly, the suggested method will o er
almost the same constant learning and computational complexity as o ered by
standard CNNs and extended to any graph structures. The experiments carried
on MNIST and Pascal VOC 2012 datasets depict the ability and e ciency of the
proposed deep network to learn the statistical and compositional features of these
high-dimensional irregular domains as represented through graphs.
