Robust and unbiased positive and unlabeled learning

Positive and unlabeled learning (PU learning) is a highly effective classification method that only involves positive and unlabeled samples. It has garnered significant attention in recent years due to its ability to greatly improve classification performance when negative samples are absent. However, numerous contributions in this field remain theoretical and fail to perform well on actual data polluted by noise. How to deal with these challenges is currently a hot research topic. Inspirited by the previous work, we propose a noise-insensitive and unbiased classification method to deal with noise data, i.e., Pinball Loss Factorization and Centroid Smoothing, called Pin-LFCS. For nonlinear situation, we also present an extended kernelized version named Pin-KLFCS. Theoretically, we investigate the property of our proposed methods, including noise insensitivity and intra-class scatter minimization. Moreover, generalization error bounds are derived to ensure their validity. Experimentally, through extensive experiments on 14 benchmark datasets with varying levels of noise, we demonstrate the efficacy and validity of our proposed methods, which outperform the existing advanced methods.