RankSVM

RankSVM, also known as Ranking SVM or SVM Rank, is a supervised learning-to-rank algorithm that learns a ranking function by optimizing pairwise preferences under a large-margin framework. Given items with relevance labels for a query, RankSVM constructs all or a subset of item pairs (i, j) such that i is more relevant than j. The model assumes a linear scoring function f(x) = w^T x; for each preferred pair, it enforces f(x_i) > f(x_j) with margin.

Equivalently, it trains a binary SVM on the difference feature vectors z_ij = x_i - x_j with label y_ij = +1 for preferred pairs. The optimization minimizes 1/2 ||w||^2 + C sum ξ_ij subject to w^T (x_i - x_j) ≥ 1 − ξ_ij, ξ_ij ≥ 0. Inference scores items by their f(x) and sorts them to produce a ranking for each query.

Training can be expensive because the number of pairs grows quadratically with the number of items; practical implementations generate pairs per query and may sample to reduce complexity. Regularization via C and feature design affect performance.

RankSVM is widely used in information retrieval, search engines, and recommendation systems, where metrics like NDCG or MAP are evaluated on rankings. It typically yields robust performance and a direct optimization target for ranking, but it does not explicitly optimize listwise metrics unless extended; it also requires labeled relevance judgments and can be computationally demanding for large-scale problems. Related methods include RankBoost, ListNet, and other learning-to-rank approaches.