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.