Torus Principal Component Analysis with an Application to RNA Structures

Understand

There are several cutting edge applications needing PCA methods for data on tori and we propose a novel torus-PCA method with important properties that can be generally applied.

• There are two existing general methods: tangent space PCA and geodesic PCA.
• However, unlike tangent space PCA, our torus-PCA honors the cyclic topology of the data space whereas, unlike geodesic PCA, our torus-PCA produces a variety of non-winding, non-dense descriptors.
• This is achieved by deforming tori into spheres and then using a variant of the recently developed principle nested spheres analysis.