Convolutional Neural Networks on Manifolds and Graphs
In the recent years, deep learning methods have literally shaken many fields of research. In computer vision, deep convolutional neural networks (CNN) have achieved unprecedented performance on the ImageNet object classification challenge, as of today already going beyond human capabilities. Though these methods have been known from the late 1980s, the computational power of modern computers, availability of large datasets, and efficient stochastic optimization methods allowed creating and effectively training complex network models that made a qualitative breakthrough in performance. However, so far the adoption of deep learning, and in particular CNN paradigms, has been notoriously lagging behind in other fields such as computer graphics and graph analysis. The main reason is that the non-Euclidean geometric structure of objects dealt with in these respective fields makes the very definition of convolution rather elusive. Given the great success of CNNs in computer vision, one could expect that devising a non-Euclidean formulation of CNN should lead to a breakthrough in these fields.
The goal of this project is to generalize convolutional neural network, a successful deep learning model, to data arising from non-Euclidean domains such as manifolds or graphs. The proposed framework will be tested on applications from the domains of computer graphics, vision, and social network analysis.