Probability-Density-aware Semi-supervised Learning

Abstract

In Semi-supervised learning(SSL), we always accept cluster assumption, assuming features in different high-density regions belong to other categories. However, it is always ignored by existing algorithms and needs mathematical explanations. This paper first proposes a theorem to statistically explain cluster assumption and prove that the probability density can significantly help to use the prior fully. A Probability-Density-Aware Measure(PM) is proposed based on the theorem to discern the similarity between neighbor points. The PM is deployed to improve Label Propagation and a new pseudo-labeling algorithm, the Probability-Density-Aware Label Propagation(PMLP), is proposed. We also prove that traditional first-order similarity pseudo-labeling could be viewed as a particular case of PMLP, which provides a comprehensive theoretical understanding of PMLP's superior performance. Extensive experiments demonstrate that PMLP achieves outstanding performance compared with other recent methods.