# Relaxed 2-D Principal Component Analysis by $L_p$ Norm for Face Recognition

## TL;DR

This paper introduces a relaxed 2D PCA method that incorporates label information and $L_p$ norms to improve face recognition accuracy, outperforming existing techniques.

## Contribution

It proposes a novel R2DPCA approach using label-based relaxation vectors and $L_p$ norms, enhancing recognition performance over traditional 2DPCA methods.

## Key findings

- R2DPCA achieves higher recognition rates than state-of-the-art methods.
- The method demonstrates high generalization ability on practical face datasets.
- Optimal $L_p$-norms are effectively selected within a reasonable range.

## Abstract

A relaxed two dimensional principal component analysis (R2DPCA) approach is proposed for face recognition. Different to the 2DPCA, 2DPCA-$L_1$ and G2DPCA, the R2DPCA utilizes the label information (if known) of training samples to calculate a relaxation vector and presents a weight to each subset of training data. A new relaxed scatter matrix is defined and the computed projection axes are able to increase the accuracy of face recognition. The optimal $L_p$-norms are selected in a reasonable range. Numerical experiments on practical face databased indicate that the R2DPCA has high generalization ability and can achieve a higher recognition rate than state-of-the-art methods.