We describe an algorithm for support vector machines (SVM) that can be parallelized efficiently and scales to very large problems with hundreds of thousands of training vectors. Instead of analyzing the whole training set in one optimization step, the data are split into subsets and optimized separately with multiple SVMs. The partial results are combined and filtered again in a'Cascade' of SVMs, until the global optimum is reached. The Cascade SVM can be spread over multiple processors with minimal communication overhead and requires far less memory, since the kernel matrices are much smaller than for a regular SVM. Convergence to the global optimum is guaranteed with multiple passes th rough the Cascade, but already a single pass provides good generalization. A single pass is 5x - 10x faster than a regular SVM for problems of 100,000 vectors when implemented on a single processor. Parallel implementations on a cluster of 16 processors were tested with over 1 million vectors (2-class problems), converging in a day or two, while a regular SVM never converged in over a week.

We study a method of optimal data-driven aggregation of classifiers in a convex combination and establish tight upper bounds on its excess risk with respect to a convex loss function under the assumption that the solution of optimal aggregation problem is sparse. We use a boosting type algorithm of optimal aggregation to develop aggregate classifiers of activation patterns in fMRI based on locally trained SVM classifiers. The aggregation coefficients are then used to design a "boosting map" of the brain needed to identify the regions with most significant impact on classification.

We show that anomaly detection can be interpreted as a binary classification problem. Using this interpretation we propose a support vector machine (SVM) for anomaly detection. We then present some theoretical results which include consistency and learning rates. Finally, we experimentally compare our SVM with the standard one-class SVM.

This paper investigates a new learning model in which the input data is corrupted with noise. We present a general statistical framework to tackle this problem. Based on the statistical reasoning, we propose a novel formulation of support vector classification, which allows uncertainty in input data. We derive an intuitive geometric interpretation of the proposed formulation, and develop algorithms to efficiently solve it. Empirical results are included to show that the newly formed method is superior to the standard SVM for problems with noisy input.

We consider the problem of deriving class-size independent generalization bounds for some regularized discriminative multi-category classification methods. In particular, we obtain an expected generalization bound for a standard formulation of multi-category support vector machines. Based on the theoretical result, we argue that the formulation over-penalizes misclassification error, which in theory may lead to poor generalization performance. A remedy, based on a generalization of multi-category logistic regression (conditional maximum entropy), is then proposed, and its theoretical properties are examined.

We establish learning rates to the Bayes risk for support vector machines (SVMs) with hinge loss. In particular, for SVMs with Gaussian RBF kernels we propose a geometric condition for distributions which can be used to determine approximation properties of these kernels. Finally, we compare our methods with a recent paper of G. Blanchard et al..

We devise and experiment with a dynamical kernel-based system for tracking hand movements from neural activity. The state of the system corresponds to the hand location, velocity, and acceleration, while the system's input are the instantaneous spike rates. The system's state dynamics is defined as a combination of a linear mapping from the previous estimated state and a kernel-based mapping tailored for modeling neural activities. In contrast to generative models, the activity-to-state mapping is learned using discriminative methods by minimizing a noise-robust loss function. We use this approach to predict hand trajectories on the basis of neural activity in motor cortex of behaving monkeys and find that the proposed approach is more accurate than both a static approach based on support vector regression and the Kalman filter.

We present an algorithm based on convex optimization for constructing kernels for semi-supervised learning. The kernel matrices are derived from the spectral decomposition of graph Laplacians, and combine labeled and unlabeled data in a systematic fashion. Unlike previous work using diffusion kernels and Gaussian random field kernels, a nonparametric kernel approach is presented that incorporates order constraints during optimization. This results in flexible kernels and avoids the need to choose among different parametric forms. Our approach relies on a quadratically constrained quadratic program (QCQP), and is computationally feasible for large datasets. We evaluate the kernels on real datasets using support vector machines, with encouraging results.

The standard approach to the classification of objects is to consider the examples as independent and identically distributed (iid). In many real world settings, however, this assumption is not valid, because a topographical relationship exists between the objects. In this contribution we consider the special case of image segmentation, where the objects are pixels and where the underlying topography is a 2D regular rectangular grid. We introduce a classification method which not only uses measured vectorial feature information but also the label configuration within a topographic neighborhood. Due to the resulting dependence between the labels of neighboring pixels, a collective classification of a set of pixels becomes necessary. We propose a new method called'Topographic Support Vector Machine' (TSVM), which is based on a topographic kernel and a self-consistent solution to the label assignment shown to be equivalent to a recurrent neural network. The performance of the algorithm is compared to a conventional SVM on a cell image segmentation task.

In this paper we show that it is possible to model sensory impressions of consumers about beef meat. This is not a straightforward task; the reason is that when we are aiming to induce a function that maps object descriptions into ratings, we must consider that consumers' ratings are just a way to express their preferences about the products presented in the same testing session. Therefore, we had to use a special purpose SVM polynomial kernel. The training data set used collects the ratings of panels of experts and consumers; the meat was provided by 103 bovines of 7 Spanish breeds with different carcass weights and aging periods. Additionally, to gain insight into consumer preferences, we used feature subset selection tools. The result is that aging is the most important trait for improving consumers' appreciation of beef meat.