Probabilistic Principal Curves on Riemannian Manifolds

This repo provides functions implementing Probabilistic Principal Curves on Riemannian Manifolds (abbreviated as PPC) using statistical software R.

Overview

There are four files implementing PPC on three spaces.

• generics.R : defines generic functions. e.g. PPC DIST LOG etc.

• ppc_euc.R : building block for implementing PPC in 2D and 3D Euclidean space.

• half-plane/half_plane_funs.R : PPC in the Poincare half-plane (2D hyperbolic space)

• sphere-2-3/sphere_funs.R : PPC in the 2D and 3D sphere

• so3-group/so3_funs.R : PPC in the 3D special orthogonal group SO(3)

Note that description of each function is provided as comment in each file. (Some are missing)

Additionaly, following files are for simulation & comparison with other methods.

• half-plane/half_plane_simulations.R
  • simulates 4 datasets on the half-plane
  • compares PPC with existing methods visually
• sphere-2-3/sphere2_simulations.R
  • simulates 2 datasets on the 2D sphere
  • compares PPC with existing methods visually
• sphere-2-3/compare.R
  • compare wave data on 2D sphere on several methods numerically
• sphere-2-3/simplex3_funs.R
  • defines simplex3 class and plot method for the class
• so3-group/so3_simulations.R
  • simulates 2 datasets on the 3D special orthogonal group

We also provide code that was used to extract election data from the excel files provided by National Election Commission of South Korea. Excel files are in ./sphere-2-3/data.

• sphere-2-3/real_data.R
  • extracts data from excel files in sphere-2-3/data and save as sphere-2-3/19pe.csv
  • fit PPC to the data, and plot
  • conducts dimension reduction using the fitted PPC
• sphere-2-3/19pe.csv
  • the real data used for analysis; can also be generated using sphere-2-3/real_data.R

Reference

• Seungwoo Kang and Hee-Seok Oh. (2024) Probabilistic Principal Curves on Riemannian Manifolds. IEEE Transactions on Pattern Analysis and Machine Intelligence 46(7), 4843-4849.