Robust 2DPCA by Tℓ₁ Criterion Maximization for Image Recognition

Two-dimensional principal component analysis (2DPCA) has been widely used to extract image features. As opposed to PCA, 2DPCA directly treats 2D matrices to extract image features instead of transforming 2D matrices into vectors. However, the classical 2DPCA based on
$F$
-norm square is sensitive to noise. To handle this problem, 2DPCAs based on
$\ell _{1}$
-norm,
$\ell _{p}$
-norm, and other norms have been studied. In this paper, as a further development, 2DPCA based on
$\text{T}\ell _{1}$
criterion is proposed, referred as 2DPCA-
$\text{T}\ell _{1}$
. Notice that, different from some norms used before,
$\text{T}\ell _{1}$
criterion is bounded and Lipschitz-continuous. So it can be expected that our 2DPCA-
$\text{T}\ell _{1}$
should be more robust. In fact, the experimental results have shown that its performance is superior to that of classical 2DPCA, 2DPCA-L1, 2DPCAL1-S, N-2-DPCA, G2DPCA, and Angle-2DPCA.