SVMrank

SVMrank is a supervised learning-to-rank algorithm based on a support vector machine framework, designed for ranking documents in response to a set of queries. It learns a scoring function that assigns a real-valued score to each query-document pair, such that documents more relevant to a query receive higher scores than less relevant ones.

In training, SVMrank uses pairwise preferences derived from labeled relevance judgments. For each query, every more relevant document d+ is paired with a less relevant document d−, and the algorithm enforces a margin constraint: f(q, d+) − f(q, d−) ≥ 1 − ξ, where f(q, d) = w · x(q, d) is the score produced by a linear model and x(q, d) is the feature vector representing the query-document pair. ξ are slack variables allowing for misorderings, and C controls the trade-off between margin size and training error. The objective is to minimize 0.5||w||^2 + C∑ξ, subject to the pairwise constraints. The result is a linear scoring function; documents are ranked for each query by sorting their scores.

SVMrank is commonly used with a linear kernel due to the high dimensionality of pairwise features, though kernel extensions exist in principle. It relies on engineered features that capture query-document characteristics (for example, term statistics, document length, and other relevance signals).

Historically developed by Thorsten Joachims, SVMrank has served as a widely cited baseline in learning-to-rank research and practical information-retrieval applications. It emphasizes robustness and interpretability of the learned linear ranking function, but it is typically outperformed by newer listwise methods on modern datasets.