  Principal component analysis (PCA) frequently suffers from the disturbance of
outliers and thus a spectrum of robust extensions and variations of PCA have
been developed. However, existing extensions of PCA treat all samples equally
even those with large noise. In this paper, we first introduce a general
collaborative-robust weight learning framework that combines weight learning
and robust loss in a non-trivial way. More significantly, under the proposed
framework, only a part of well-fitting samples are activated which indicates
more importance during training, and others, whose errors are large, will not
be ignored. In particular, the negative effects of inactivated samples are
alleviated by the robust loss function. Then we furthermore develop an enhanced
PCA which adopts a point-wise sigma-loss function that interpolates between
L_2,1-norm and squared Frobenius-norm and meanwhile retains the rotational
invariance property. Extensive experiments are conducted on occluded datasets
from two aspects including reconstructed errors and clustering accuracy. The
experimental results prove the superiority and effectiveness of our model.
