Functional Bipartite Ranking: a Wavelet-Based Filtering Approach
This work addresses ranking issues in functional data analysis, which is incremental as it adapts existing multivariate ranking methods to functional contexts.
The paper tackles the bipartite ranking problem for functional data by learning a scoring function with optimal ROC curve, using wavelet-based approximations to select compact representations of input curves and achieving competitive performance in numerical experiments.
It is the main goal of this article to address the bipartite ranking issue from the perspective of functional data analysis (FDA). Given a training set of independent realizations of a (possibly sampled) second-order random function with a (locally) smooth autocorrelation structure and to which a binary label is randomly assigned, the objective is to learn a scoring function s with optimal ROC curve. Based on linear/nonlinear wavelet-based approximations, it is shown how to select compact finite dimensional representations of the input curves adaptively, in order to build accurate ranking rules, using recent advances in the ranking problem for multivariate data with binary feedback. Beyond theoretical considerations, the performance of the learning methods for functional bipartite ranking proposed in this paper are illustrated by numerical experiments.