signal-processing

This repository gathers implementations of machine learning algorithms for signal processing using Python from scratch.

Coming next: isomap, and locally linear embedding (LLE) for dimensionality reduction with manifold learning.

Dimensionality Reduction

The following will run the PCA demo from the first article:

python -c 'from dimensionality_reduction import demo; demo()'

This performs PCA on the 982 MNIST images of the number 4, and saves a sample reconstruction from reduced images with 2, 16, 64 and 256 principal components.

Input image:

Reconstruction with 2, 16, 64, 128 principal components:

Manifold learning

Isomap and LLE are implemented for manifold learning. The following will run the demo from the second article:

python dimensionality_reduction.py

This performs PCA, Isomap and LLE on the 892 MNIST images of the number 5 and saves the 2D projection of the data points.

PCA projection:

Isomap projection:

LLE projection:

Source Separation

Independent Components Analysis and Nonnegative Matrix Factorization are implemented for source separation. The following will run the demo:

python source_separation.py

This performs ICA and NMF on 1000 MNIST images of the numbers 0, 1, 4, 7 that have been mixed together with varying ratio, and saves the extracted source images.

Input images:

Source separation with ICA:

Source separation with NMF: