Learning From N-Tuple Similarities and Unlabeled Data

Learning from pairwise similarity and unlabeled data (SU) is a recently emerging weakly-supervised learning method, which learns a classifier from similar data pairs (two instances belonging to the same class) and unlabeled data. However, this framework is insoluble for triplet similarities and unlabeled data. To address this limitation, this article develops a framework for learning from triplet similarities (three instances belonging to the same class) and unlabeled data points, denoted as TSU. This framework not only showcases the feasibility of constructing a TSU classifier but also serves as an inspiration to explore the broader challenge of addressing N-tuple similarities (N ≥ 2) and unlabeled data points. To tackle this more generalized problem, the present article develops an advancing weakly-supervision framework of learning from N-tuple similarities (N instances belong to the same class) and unlabeled data points, named NSU. This framework provides a solid foundation for handling diverse similarity scenarios. Based on these findings, we propose empirical risk minimization estimators for both TSU and NSU classification. The estimation error bounds are also established for the proposed methods. Finally, experiments are performed to verify the effectiveness of the proposed algorithm.