Low-Rank Matrix Restoration

Introduction

This project focuses on low-rank matrix restoration with robust principal component analysis (RPCA) and matrix completion (MC). We have implemented the following algorithms.

• PCA
• Robust PCA
  • Gradient descent (with Adam)
  • Augmented Lagrange multipliers
  • Accelerated proximal gradient
  • Singular value thresholding
• Matrix Completion
  • Alternating direction method
  • Singular value thresholding
  • Probabilistic matrix factorization
  • Biased probabilistic matrix factorization
  • Neural tangent kernels

Structure

The directory of this project is listed as follows.

|- bin/
|- data/
|- doc/
|- ntk/
|- pre/
|- utils/
|- README.md
|- requirements.txt

File Descriptions

• bin/
  • This folder contains the executable code files
• data/
  • This folder contains images and results
• doc/
  • This folder contains the report of this project written with LaTeX
• ntk/
  • This folder is taken from [link]
• pre/
  • This folder contains the presentation slides.
• utils/
  • This folder contains utilities of this project
• README.md
  • This file serves as user manual of this project
• requirements.txt
  • This file contains python packages used in this project

Quick Start

1. Please install required packages included in requirements.txt via pip.

~$ pip install -r requirements.txt

1. Kindly run bin/low_rank_re.py to test all algorithms on images in data/.

~$ cd bin
~bin$ python low_rank_re.py

1. Please run bin/results_analysis.ipynb to analyze the results and plot figures.

Results

PCA

Robust PCA

Matrix Completion

References

• https://github.com/dganguli/robust-pca
• https://github.com/tonyduan/matrix-completion
• https://github.com/uhlerlab/ntk_matrix_completion
• https://github.com/stephenbeckr/fastRPCA
• https://github.com/dfm/pcp
• https://github.com/jkarnows/rpcaADMM
• https://www.dorukhanserg.in/post/implementing-rpca/
• https://stackoverflow.com/questions/40721260/how-to-use-robust-pca-output-as-principal-component-eigenvectors-from-traditio
• http://jeankossaifi.com/blog/rpca.html
• http://blog.shriphani.com/2013/12/18/robust-principal-component-pursuit-background-matrix-recovery/
• https://github.com/sagarvegad/Adam-optimizer
• https://people.eecs.berkeley.edu/~yima/matrix-rank/sample_code.html
• https://zhouchenlin.github.io/