For a given set of subtopic candidates with annotated subtopics, {(Sn, yn)} (1≤n≤N), we need to estimate the optimal weight w. Empirically, the optimal weight w should minimize the error between the predicted partition y ' and the true partition y, and it should also have a good generalization capability.
it is learnt by solving the following optimization problem (Yu and Joachims, 2009 where ∆(yn, y ' , h ' ) indicates a loss between a true partition yn and the predicted partition y ' specified by h ' , ξn (1≤n≤N) is a set of slack variables to allow errors in the training data, and C controls the trade-off between empirical loss and model complexity.