14 citations · 58 across the 16 of their papers we have counts for
10 papers · 1 filter
Higher Order Gauge Equivariant CNNs on Riemannian Manifolds and Applications
Gianfranco Cortes, Yue Yu, Robin Chen +3
With the advent of group equivariant convolutions in deep networks literature, spherical CNNs with -equivariant layers have been developed to cope with data that ar…
VolterraNet: A higher order convolutional network with group equivariance for homogeneous manifolds
Monami Banerjee, Rudrasis Chakraborty, Jose Bouza +1
Convolutional neural networks have been highly successful in image-based learning tasks due to their translation equivariance property. Recent work has generalized the traditional…
Nested Grassmannians for Dimensionality Reduction with Applications
Chun-Hao Yang, Baba C. Vemuri
In the recent past, nested structures in Riemannian manifolds has been studied in the context of dimensionality reduction as an alternative to the popular principal geodesic analys…
MVC-Net: A Convolutional Neural Network Architecture for Manifold-Valued Images With Applications
Jose J. Bouza, Chun-Hao Yang, David Vaillancourt +1
Geometric deep learning has attracted significant attention in recent years, in part due to the availability of exotic data types for which traditional neural network architectures…
ManifoldNet: A Deep Network Framework for Manifold-valued Data
Rudrasis Chakraborty, Jose Bouza, Jonathan Manton +1
Deep neural networks have become the main work horse for many tasks involving learning from data in a variety of applications in Science and Engineering. Traditionally, the input t…
Dictionary Learning and Sparse Coding on Statistical Manifolds
Rudrasis Chakraborty, Monami Banerjee, Baba C. Vemuri
In this paper, we propose a novel information theoretic framework for dictionary learning (DL) and sparse coding (SC) on a statistical manifold (the manifold of probability distrib…
A CNN for homogneous Riemannian manifolds with applications to Neuroimaging
Rudrasis Chakraborty, Monami Banerjee, Baba C. Vemuri
Convolutional neural networks are ubiquitous in Machine Learning applications for solving a variety of problems. They however can not be used in their native form when the domain o…
Statistics on the (compact) Stiefel manifold: Theory and Applications
Rudrasis Chakraborty, Baba Vemuri
A Stiefel manifold of the compact type is often encountered in many fields of Engineering including, signal and image processing, machine learning, numerical optimization and other…
An information theoretic formulation of the Dictionary Learning and Sparse Coding Problems on Statistical Manifolds
Rudrasis Chakraborty, Monami Banerjee, Victoria Crawford +1
In this work, we propose a novel information theoretic framework for dictionary learning (DL) and sparse coding (SC) on a statistical manifold (the manifold of probability distribu…
An efficient Exact-PGA algorithm for constant curvature manifolds
Rudrasis Chakraborty, Dohyung Seo, Baba C. Vemuri
Manifold-valued datasets are widely encountered in many computer vision tasks. A non-linear analog of the PCA, called the Principal Geodesic Analysis (PGA) suited for data lying on…