Journal article

ManifoldNet: A Deep Neural Network for Manifold-valued Data with Applications

Rudrasis Chakraborty, Jose Bouza, Jonathan Manton, Baba C Vemuri

IEEE Transactions on Pattern Analysis and Machine Intelligence | Institute of Electrical and Electronics Engineers (IEEE) | Published : 2020

Abstract

Geometric deep learning is a relatively nascent field that has attracted significant attention in the recent past. This is partly due to the ready availability of manifold-valued data. In this paper we present a novel theoretical framework for developing deep neural networks to cope with manifold-valued fields as inputs. We also present a novel architecture to realize this theory and call it a ManifoldNet. Analogous to convolutions in vector spaces which are equivalent to computing weighted sums, manifold-valued data ‘convolutions’ can be defined using the weighted Frechet Mean (wFM), an intrinsic operation. The hidden layers of ManifoldNet compute wFM of their inputs, where the weights are ..

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