Binary classification from N-Tuple Comparisons data

Pairwise comparison classification (Pcomp) is a recently thriving weakly-supervised method that generates a binary classifier based on feedback information from comparisons between unlabeled data pairs (one is more likely to be positive than the other). However, this approach turns out challenging in more complex scenarios involving comparisons among more than two instances. To overcome this problem, this paper starts with a comprehensive exploration of the triplet comparisons data (the first instance is more likely to be positive than the second instance, and the second instance is more likely to be positive than the third instance). Then the problem is extended to investigate $N$-Tuple comparisons learning (NT-Comp: the confidence of belonging to the positive class from the first instance to the last instance is in descending order, with the first instance being the biggest). This generalized model accommodates not only pairwise comparisons data but also more than two comparisons data. This paper derives an unbiased risk estimator for $N$-Tuple comparisons learning. The estimation error bound is also established theoretically. Finally, an experiment is conducted to validate the effectiveness of the proposed method.