  We propose a new data mining approach in ranking documents based on the
concept of cone-based generalized inequalities between vectors. A partial
ordering between two vectors is made with respect to a proper cone and thus
learning the preferences is formulated as learning proper cones. A pairwise
learning-to-rank algorithm (ConeRank) is proposed to learn a non-negative
subspace, formulated as a polyhedral cone, over document-pair differences. The
algorithm is regularized by controlling the `volume' of the cone. The
experimental studies on the latest and largest ranking dataset LETOR 4.0 shows
that ConeRank is competitive against other recent ranking approaches.
