LPCA: Visualization of high-dimensional datasets using Local Principal Component Analysis
Introduction
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LPCA is a visualization procedure implemented by Alice Barbara Tumpach that computes 2D positions of labelled datapoints from a high-dimensional dataset by performing a global Principal Component Analysis (PCA) followed by local PCAs in each class. The low-dimensional approximation of each class is then glued in the plane spanned by the first two eigenvalues of the global PCA in such a way that:
- 1. the distance from the global mean (placed at the origin) to the mean of each class is preserved
- 2. the direction from the global mean to the mean of each class is preserved
- 3. the angle between the main eigenvector of each class and the main eigenvector of the whole dataset is preserved.
Code
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The code is available as a Matlab function at https://github.com/Tumpach/LPCA
Demonstration of the program
On 6000 fashion items from Fashion MNIST dataset:
On the whole Fashion MNIST dataset (LPCA takes 3 seconds on a Mac M1, tSNE much more, mdscale does not converge in a reasonable amount of time...):
On 6000 digits from MNIST dataset:
On 50000 digits from MNIST dataset (mdscale takes too much time...):
