| title | author |
|---|---|
pyPNS README |
Zhiyuan Liu (zhiy at cs dot unc dot edu) |
[TOC]
This is python implementation of Principal Nested Spheres (PNS). Please refer to the following paper for technical and application details.
Jung et al., Analysis of principal nested spheres. Kim et al., Small‐sphere distributions for directional data with application to medical imaging.
The following figure shows the simulated data (shown as blue points) that distribute along a small circle on toy_example_small_circle.mat.
Fitting with a PNS model to the data leads to more useful variation directions. As a result, the majority (~98%) of the variation can be captured in the first principal component; see the left on the following figure. As a comparison, Principal Component Analysis (PCA) needs more components.
The bars are the percentage of the explained variance by each principal component. The red curve is the cumulative explained variance.
pns_test.py: This is the demo application of PNS. A user may refer the code for the usage of the PNS fitting.
principal_nested_spheres.py: This is the major module that implements interfaces of fitting PNS to data.
utils.py: This file provides some handy functions for operations on hyperspheres.
toy_example_small_circle.mat: This is the toy example data used in the pns_test.py.
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