  In this article we propose a novel ranking algorithm, referred to as HierLPR,
for the multi-label classification problem when the candidate labels follow a
known hierarchical structure. HierLPR is motivated by a new metric called eAUC
that we design to assess the ranking of classification decisions. This metric,
associated with the hit curve and local precision rate, emphasizes the accuracy
of the first calls. We show that HierLPR optimizes eAUC under the tree
constraint and some light assumptions on the dependency between the nodes in
the hierarchy. We also provide a strategy to make calls for each node based on
the ordering produced by HierLPR, with the intent of controlling FDR or
maximizing F-score. The performance of our proposed methods is demonstrated on
synthetic datasets as well as a real example of disease diagnosis using NCBI
GEO datasets. In these cases, HierLPR shows a favorable result over competing
methods in the early part of the precision-recall curve.
