@CONFERENCE\{IMM2009-05751, author = "V. Potluru and S. Plis and M. M{\o}rup and V. Calhoun and T. Lane", title = "Efficient Multiplicative updates for Support Vector Machines", year = "2009", booktitle = "Siam {SDM} 09", volume = "", series = "", editor = "", publisher = "", organization = "", address = "", url = "http://www2.compute.dtu.dk/pubdb/pubs/5751-full.html", abstract = "The dual formulation of the support vector machine (SVM) objective function is an instance of a nonnegative quadratic programming problem. We reformulate the {SVM} objective function as a matrix factorization problem which establishes a connection with the regularized nonnegative matrix factorization (NMF) problem. This allows us to derive a novel multiplicative algorithm for solving hard and soft margin {SVM}. The algorithm follows as a natural extension of the updates for {NMF} and semi-NMF. No additional parameter setting, such as choosing learning rate, is required. Exploiting the connection between {SVM} and {NMF} formulation, we show how {NMF} algorithms can be applied to the {SVM} problem. Multiplicative updates that we derive for {SVM} problem also represent novel updates for semi-NMF. Further this unified view yields algorithmic insights in both directions: we demonstrate that the Kernel Adatron algorithm for solving SVMs can be adapted to {NMF} problems. Experiments demonstrate rapid convergence to good classifiers. We analyze the rates of asymptotic convergence of the updates and establish tight bounds. We test them on several datasets using various kernels and report equivalent classification performance to that of a standard {SVM}." }