A CASE STUDY ON SUPPORT VECTOR MACHINES VERSUS ARTIFICIAL NEURAL NETWORKS

The capability of artificial neural networks for pattern recognition of real world problems is well known. In recent years, the support vector machine has been advocated for its structure risk minimization leading to tolerance margins of decision boundaries. Structures and performances of these pattern classifiers depend on the feature dimension and training data size. The objective of this research is to compare these pattern recognition systems based on a case study. The particular case considered is on classification of hypertensive and normotensive right ventricle (RV) shapes obtained from Magnetic Resonance Image (MRI) sequences. In this case, the feature dimension is reasonable, but the available training data set is small, however, the decision surface is highly nonlinear.For diagnosis of congenital heart defects, especially those associated with pressure and volume overload problems, a reliable pattern classifier for determining right ventricle function is needed. RV¡¦s global and regional surface to volume ratios are assessed from an individual¡¦s MRI heart images. These are used as features for pattern classifiers. We considered first two linear classification methods: the Fisher linear discriminant and the linear classifier trained by the Ho-Kayshap algorithm. When the data are not linearly separable, artificial neural networks with back-propagation training and radial basis function networks were then considered, providing nonlinear decision surfaces. Thirdly, a support vector machine was trained which gives tolerance margins on both sides of the decision surface. We have found in this case study that the back-propagation training of an artificial neural network depends heavily on the selection of initial weights, even though randomized. The support vector machine where radial basis function kernels are used is easily trained and provides decision tolerance margins, in spite of only small margins

Training Support Vector Machines Using Frank-Wolfe Optimization Methods

Training a Support Vector Machine (SVM) requires the solution of a quadratic programming problem (QP) whose computational complexity becomes prohibitively expensive for large scale datasets. Traditional optimization methods cannot be directly applied in these cases, mainly due to memory restrictions. By adopting a slightly different objective function and under mild conditions on the kernel used within the model, efficient algorithms to train SVMs have been devised under the name of Core Vector Machines (CVMs). This framework exploits the equivalence of the resulting learning problem with the task of building a Minimal Enclosing Ball (MEB) problem in a feature space, where data is implicitly embedded by a kernel function. In this paper, we improve on the CVM approach by proposing two novel methods to build SVMs based on the Frank-Wolfe algorithm, recently revisited as a fast method to approximate the solution of a MEB problem. In contrast to CVMs, our algorithms do not require to compute the solutions of a sequence of increasingly complex QPs and are defined by using only analytic optimization steps. Experiments on a large collection of datasets show that our methods scale better than CVMs in most cases, sometimes at the price of a slightly lower accuracy. As CVMs, the proposed methods can be easily extended to machine learning problems other than binary classification. However, effective classifiers are also obtained using kernels which do not satisfy the condition required by CVMs and can thus be used for a wider set of problems