Curvilinear Component Analysis implementation for Python.
This code was implemented using the following article https://ieeexplore.ieee.org/document/554199 and the book "Nonlinear Dimensionality Reduction" by Michel Verleysen, John A. R. Lee.
Curvilinear Component Analysis (CCA) is a Non-linear Dimensionality Reduction technic, basead on the distance betweens the points: it tries to create a new space, with a small dimension, which the distance betweens points are equal in the original space (if this distance is smaller than Lambda, one of the parameters of the algorithm).
The author from the article tests the algorithm in 3 artificials examples, with 500 points each: sphere, U-fold and two circles. All these tests tries to reduce a 3 dimensional data to a 2 dimensional data. The results from my implementation are show in the following subsections.
The original space:
The dy dx representation after CCA training:
The reduced space:
The original space:
The dy dx representation after CCA training:
The reduced space:
The original space:
The dy dx representation after CCA training:
The reduced space:
