Support Vector Machines (SVMs) for regression problems are trained by solving a quadratic optimization problem which needs on the order of l 2 memory and time resources to solve, where l is the number of training examples. In this paper, we propose a decomposition algorithm, SVMTorch 1 , which is similar to SVM-Light proposed by Joachims (1999) for classification problems, but adapted to regression problems. With this algorithm, one can now efficiently solve large-scale regression problems (more than 20000 examples). Comparisons with Nodelib, another publicly available SVM algorithm for large-scale regression problems from Flake and Lawrence (2000) yielded significant time improvements. Finally, based on a recent paper from Lin (2000), we show that a convergence proof exists for our algorithm. 1. Introduction Vapnik (1995) has proposed a method to solve regression problems using support vector machines. It has yielded excellent performance on many regression and time ser...

Abstract—We propose a learning approach to tracking explicitly minimizing the computational complexity of the tracking process subject to user-defined probability of failure (loss-of-lock) and precision. The tracker is formed by a Number of Sequences of Learned Linear Predictors (NoSLLiP). Robustness of NoSLLiP is achieved by modeling the object as a collection of local motion predictors— object motion is estimated by the outlier-tolerant RANSAC algorithm from local predictions. The efficiency of the NoSLLiP tracker stems 1) from the simplicity of the local predictors and 2) from the fact that all design decisions, the number of local predictors used by the tracker, their computational complexity (i.e., the number of observations the prediction is based on), locations as well as the number of RANSAC iterations, are all subject to the optimization (learning) process. All time-consuming operations are performed during the learning stage—tracking is reduced to only a few hundred integer multiplications in each step. On PC with 1xK8 3200+, a predictor evaluation requires about 30 s. The proposed approach is verified on publicly available sequences with approximately 12,000 frames with ground truth. Experiments demonstrate superiority in frame rates and robustness with respect to the SIFT detector, Lucas-Kanade tracker, and other trackers. Index Terms—Image processing and computer vision, scene analysis, tracking. Ç 1

This paper presents a new approach to time series modeling using the Support Vector Method (SVM). Whereas the γ-filter can provide stability in several time series models, the SVM is proposed here to provide robustness in the estimation of the γ-filter coefficients. An Iterated Re-Weighted Least Squares SVM efficient optimization is also presented, which avoids the use of Quadratic Programming. Several application examples (system identifcation, chaotic time-series prediction, and channel equalization) show the advantages of the joint SVM γ-filter when compared to the γ-filter alone.