  One of the most powerful methods of color image recognition is the
two-dimensional principle component analysis (2DQPCA) approach, which is based
on quaternion representation and preserves color information very well.
However, the current versions of 2DQPCA are still not feasible to extract
different geometric properties of color images according to practical data
analysis requirements and they are vulnerable to strong noise. In this paper, a
generalized 2DQPCA approach with weighting is presented with imposing $L_{p}$
norms on both constraint and objective functions. As a unit 2DQPCA framework,
this new version makes it possible to choose adaptive regularizations and
constraints according to actual applications and can extract both geometric
properties and color information of color images. The projection vectors
generated by the deflating scheme are required to be orthogonal to each other.
A weighting matrix is defined to magnify the effect of main features. This
overcomes the shortcomings of traditional 2DQPCA that the recognition rate
decreases as the number of principal components increases. The numerical
results based on the real face databases validate that the newly proposed
method is robust to noise and performs better than the state-of-the-art
2DQPCA-based algorithms and four prominent deep learning methods.
