TTPCA is a dimensionality reduction and visualization method for scalar functions that is based on the tensor train (TT) decomposition.
The method is described in the paper Visualization of High-dimensional Scalar Functions Using Principal Parameterizations:
@ARTICLE{BP:18,
author = {{Ballester-Ripoll}, R. and {Pajarola}, R.},
title = "{Visualization of High-dimensional Scalar Functions Using Principal Parameterizations}",
journal = {ArXiv e-prints},
archivePrefix = "arXiv",
eprint = {1809.03618},
primaryClass = "cs.GR",
keywords = {Computer Science - Graphics, Computer Science - Machine Learning, Computer Science - Multimedia, Computer Science - Numerical Analysis},
year = 2018,
month = sep}
TTPCA relies on ttrecipes, a library of auxiliary TT functions. Please install ttrecipes first as indicated in its README.
After installing ttrecipes, you should be able to install TTPCA as follows:
git clone https://github.com/rballester/ttpca.git
pip install -e ttpca
(note: it's always highly recommended to work in a conda or pip virtualenvironment!)
All numerical functionality is encapsulated in the function reduce(). It simply takes a TT and a list of k target variables and produces a TT with (k+1) dimensions (the last dimension has size 3) that contains the principal parameterization (i.e. embedding into a 3D Euclidean space) for those k variables:
ttpca.reduce(t, modes=[0, 1]) # This will return a parameterized surface in 3D
We provide a visualization front-end using PyQtGraph and PyOpenGL that allows 3D navigation of plot matrices, curve arrays, and various interactions as described in the paper.