Pivotal-Aware Principal Component Analysis

A conventional principal component analysis (PCA) frequently suffers from the disturbance of outliers, and thus, spectra of extensions and variations of PCA have been developed. However, all the existing extensions of PCA derive from the same motivation, which aims to alleviate the negative effect of the occlusion. In this article, we design a novel collaborative-enhanced learning framework that aims to highlight the pivotal data points in contrast. As for the proposed framework, only a part of well-fitting samples are adaptively highlighted, which indicates more significance during training. Meanwhile, the framework can collaboratively reduce the disturbance of the polluted samples as well. In other words, two contrary mechanisms could work cooperatively under the proposed framework. Based on the proposed framework, we further develop a pivotal-aware PCA (PAPCA), which utilizes the framework to simultaneously augment positive samples and constrain negative ones by retaining the rotational invariance property. Accordingly, extensive experiments demonstrate that our model has superior performance compared with the existing methods that only focus on the negative samples.