Flexible orthogonal semisupervised learning for dimension reduction with image classification

Robust Principal Component Analysis via Joint Reconstruction and Projection

Principal component analysis (PCA) is one of the most widely used unsupervised dimensionality reduction algorithms, but it is very sensitive to outliers because the squared l2 -norm is used as distance metric. Recently, many scholars have devoted themselves to solving this difficulty. They learn the projection matrix from minimum reconstruction error or maximum projection variance as the starting point, which leads them to ignore a serious problem, that is, the original PCA learns the projection matrix by minimizing the reconstruction error and maximizing the projection variance simultaneously, but they only consider one of them, which imposes various limitations on the performance of model. To solve this problem, we propose a novel robust principal component analysis via joint reconstruction and projection, namely, RPCA-RP, which combines reconstruction error and projection variance to fully mine the potential information of data. Furthermore, we carefully design a discrete weight for model to implicitly distinguish between normal data and outliers, so as to easily remove outliers and improve the robustness of method. In addition, we also unexpectedly discovered that our method has anomaly detection capabilities. Subsequently, an effective iterative algorithm is explored to solve this problem and perform related theoretical analysis. Extensive experimental results on several real-world datasets and RGB large-scale dataset demonstrate the superiority of our method.

Can the Virtual Labels Obtained by Traditional LP Approaches Be Well Encoded in WLR?

Semisupervised dimension reduction via virtual label regression first derives the virtual labels of unlabeled data by employing a newly designed label propagation (LP) approach (called Special random walk (SRW)) and then encodes them in a weighted linear regression model. Nie et al. (2011) highlighted two important characteristics of SRW nonexistent in the previous LP approaches: outlier detection and probability value output, which guarantee the elegant encoding of the resultant virtual labels in the weighted label regression. However, in this brief, we show that the relationship between the SRW and the previous work on LP is very close. Naturally, a problem deserving investigation is whether traditional LP approaches are indeed unable to share the above two characteristics of SRW. We aim to address this problem.