Probability-Density-aware Semi-supervised Learning

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.

Authors

• Shuyang Liu East China Normal University
• Ruiqiu Zheng East China Normal University
• Yunhang Shen Tencent Youtu Lab, Shanghai 200233, China.
• Zhou Yu East China Normal University
• Ke Li
• Xing Sun Tencent YouTu Lab
• Shaohui Lin East China Normal University Key Laboratory of Advanced Theory and Application in Statistics and Data Science- MOE

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