Robust Sparse Smooth Principal Component Analysis (RSSPCA)

This repository contains the implementation of Robust Sparse Smooth Principal Component Analysis (RSSPCA) for face reconstruction and recognition tasks.

Overview

RSSPCA is a novel dimensionality reduction method that combines robustness, sparsity and smoothness properties. The algorithm finds the first projection vector by solving the following optimization problem:

$$\mathop{\max}_{w} \lVert X^Tw \rVert_1, s.t. \lVert w \rVert_2^2=1, \lVert w \rVert_1<=c_1, w^TLw<=c_2$$

where:

• $c_1$ and $c_2$ are positive constants
• $L$ is a Laplacian matrix representing the two-dimensional spatial structure information of images

Features

• Robust to outliers and noise in face images
• Sparse projection vectors for efficient feature extraction
• Incorporates spatial smoothness constraints
• Suitable for both face reconstruction and recognition tasks

Experimental Validation

The algorithm was extensively evaluated on six benchmark face databases:

• AR
• FEI
• FERET
• GT
• ORL
• Yale

More benchmark face databases can be found here.

Comparison Methods

RSSPCA was compared with several state-of-the-art algorithms:

• PCA (Principal Component Analysis)
• PCA-L1
• RSPCA
• RSMPCA

Installation and Usage

1. Clone this repository:

git clone https://github.com/yuzhounh/RSSPCA.git

2. Run the demo script in MATLAB:

main.m

Parallel Implementation

For large-scale applications, a parallel computing version is available here.

Contact

Jing Wang

• Email: wangjing@xynu.edu.cn

License

Copyright (C) 2023 Jing Wang. This code is released under the BSD license.

Updates

Last updated: January 29, 2024