@TechReport{Franc-CAK-2006-22, IS = { zkontrolovano 29 Dec 2006 }, UPDATE = { 2006-05-25 }, author = {Franc, Vojt{\v e}ch and Hlav{\'a}{\v c}, V{\'a}clav}, title = {A Novel Algorithm for Learning Support Vector Machines with Structured Output Spaces}, institution = {Department of Cybernetics, Faculty of Electrical Engineering, Czech Technical University}, address = {Prague, Czech Republic}, year = {2006}, month = {May}, type = {Research Report}, number = {{K333--22/06}, {CTU--CMP--2006--04}}, pages = {21}, figures = {6}, authorship = {90-10}, psurl = {[Franc-TR-2006-04.ps]}, project = {1M0567, COSPAL IST-004176, INTAS 04-77-7347}, annote = {This report proposes a novel optimization algorithm for learning support vector machines (SVM) classifiers with structured output spaces introduced recently by Tsochantaridis et. al. Learning structural SVM classifier leads to a special instance of quadratic programming (QP) optimization with a huge number of constraints. The number of constraints is proportional to the cardinality of the output space which makes the QP task intractable by classical optimization methods. We propose a novel QP solver based on sequential minimal optimization (SMO). Unlike the original SMO, we propose a novel strategy for selecting variables to be optimized. The strategy aims at selecting such variables which yield the maximal improvement of optimization. We prove that the algorithm converges in a finite number of iterations to the solution which differs from the optimal one at most by a prescribed constant. Experiments performed show that the proposed algorithm is very competitive to a cutting plane algorithm of Tsochantaridis et. al. The proposed algorithm can be easily implemented and it does not require any external QP solver in contrary to the cutting plain algorithm. We demonstrated a capability of the algorithm on a problem of learning the Hidden Markov Network for color image segmentation and learning a structural classifier for car license plate recognition. }, keywords = {support vector machines, structural classification, quadratic programming}, }