Multi-label Classification Based on Domain Analysis in Fixed Point Method

Nowadays a multi-label classification problem arises in different areas for which the significant amount of data has been gained. This problem can be viewed as the one comprising two steps: training some ranking function sorting instances in each class and defining the optimal number of predictions for it. This paper is devoted to the second step of the optimal threshold selection while maximizing the F-macro measure. To do so, we reduce the multi-dimensional problem to the two-dimensional problem of finding a fixed point of a specifically introduced transformation defined on a unit square. We suggest the algorithm of finding the vector of optimal thresholds based on the domain analysis of the introduced transformation. Moreover, we provide the complexity estimations of the proposed algorithm. We evaluate the algorithm on the extreme classification benchmark Wikil.SHTC-325K comparing its performance with some baseline results.