11 Model Selection for Ranking SVM Using Regularization Path Karina Zapien 1 , Gilles Gasso 1 , Thomas Gärtner 2 and Stéphane Canu 1 1 LITIS EA 4108 - INSA de Rouen 2 Fraunhofer IAIS, 1 France 2 Germany 1. Introduction This chapter deals with supervised learning problems under the ranking framework. Ranking algorithms are typically introduced as a tool for personalizing the order in which document recommendations or search results - in the web, for example - are presented. That is, the more important a result is to the user, the earlier it should be listed. To this end, two possible settings can be considered : i. the algorithm tries to interactively rearrange the results of one search such that relevant results come the closer to the top the more (implicit) feedback the user provides, ii. the algorithm tries to generalize over several queries and presents the results of one search in an order depending on the feedback obtained from previous searches. The first setting deals with an active learning while the second setting deals with a passive supervised learning. This kind of problems have gain major attention given the nowadays amount of available informations. This is without doubt a challenging task in the medium and large scale context. Several methods have been proposed to solve these problems. For the passive setting, the Rankboost algorithm (Freund et al. (2003)) is an adaptation from the Adaboost algorithm to the ranking problem. This is a boosting algorithm which works by iteratively building a linear combination of several “weak” algorithms to form a more accurate algorithm. The Pranking algorithm (Crammer & Singer (2001)) is an online version of the weighted algorithm. The SVRank and RankSVMalgorithms are the adaptation of the Support Vector machines for classification and regression, respectively, while the MPRank (Cortes et al. (2007)) is a magnitude-preserving algorithm, which searches not only to keep the relative position of each sample but also to preserve the distance given by the correct ordering. This last algorithm has as well the form of a regularization problem as the two previous with a different cost function. Later, the Ranking SVM (RankSVM) algorithm was proposed by Herbrich et al. (2000) and Joachims (2002) as an optimization problem with constraints given by the induced graph of the ordered queries’ results. This algorithm forms part of the family of kernel algorithms of the SVM type (Boser et al. (1992); Schölkopf & Smola (2002)). Kernel methods like the SVM or the ranking SVM solve optimization problems of the form Open Access Database www.intechweb.org Source: Machine Learning, Book edited by: Abdelhamid Mellouk and Abdennacer Chebira, ISBN 978-3-902613-56-1, pp. 450, February 2009, I-Tech, Vienna, Austria www.intechopen.com