English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Convolutional neural networks are ubiquitous in Machine Learning applicationsfor solving a variety of problems. They however can not be used in their nativeform when the domain of the data is commonly encountered manifolds such as thesphere, the special orthogonal group, the Grassmanian, the manifold ofsymmetric positive definite matrices and others. Most recently, generalizationof CNNs to data domains such as the 2-sphere has been reported by some researchgroups, which is referred to as the spherical CNNs (SCNNs). The key property ofSCNNs distinct from CNNs is that they exhibit the rotational equivarianceproperty that allows for sharing learned weights within a layer. In this paper,we theoretically generalize the CNNs to Riemannian homogeneous manifolds, thatinclude but are not limited to the aforementioned example manifolds. Our keycontributions in this work are: (i) A theorem stating that linear groupequivariance systems are fully characterized by correlation of functions on thedomain manifold and vice-versa. This is fundamental to the characterization ofall linear group equivariant systems and parallels the widely used result inlinear system theory for vector spaces. (ii) As a corrolary, we prove theequivariance of the correlation operation to group actions admitted by theinput domains which are Riemannian homogeneous manifolds. (iii) We present thefirst end-to-end deep network architecture for classification of diffusionmagnetic resonance image (dMRI) scans acquired from a cohort of 44 ParkinsonDisease patients and 50 control/normal subjects. (iv) A proof of conceptexperiment involving synthetic data generated on the manifold of symmetricpositive definite matrices is presented to demonstrate the applicability of ournetwork to other types of domains.

A CNN for homogneous Riemannian manifolds with applications to Neuroimaging