  Bipartite ranking is a fundamental machine learning and data mining problem.
It commonly concerns the maximization of the AUC metric. Recently, a number of
studies have proposed online bipartite ranking algorithms to learn from massive
streams of class-imbalanced data. These methods suggest both linear and
kernel-based bipartite ranking algorithms based on first and second-order
online learning. Unlike kernelized ranker, linear ranker is more scalable
learning algorithm. The existing linear online bipartite ranking algorithms
lack either handling non-separable data or constructing adaptive large margin.
These limitations yield unreliable bipartite ranking performance. In this work,
we propose a linear online confidence-weighted bipartite ranking algorithm
(CBR) that adopts soft confidence-weighted learning. The proposed algorithm
leverages the same properties of soft confidence-weighted learning in a
framework for bipartite ranking. We also develop a diagonal variation of the
proposed confidence-weighted bipartite ranking algorithm to deal with
high-dimensional data by maintaining only the diagonal elements of the
covariance matrix. We empirically evaluate the effectiveness of the proposed
algorithms on several benchmark and high-dimensional datasets. The experimental
results validate the reliability of the proposed algorithms. The results also
show that our algorithms outperform or are at least comparable to the competing
online AUC maximization methods.
