Linear support vector machines (svms) have become popular for solving classification tasks due to their fast and simple online application to large scale data sets. However, many problems are not linearly separable. For these problems kernel-based svms are often used, but unlike their linear variant they suffer from various drawbacks in terms of computational and memory efficiency. Their respon...

Solving optimization models (including parameters fitting) for support vector machines on largescale training data is often an expensive computational task. This paper proposes a multilevel algorithmic framework that scales efficiently to very large data sets. Instead of solving the whole training set in one optimization process, the support vectors are obtained and gradually refined at multipl...

The support vector machine is a flexible optimization-based technique widely used for classification problems. In practice, its training part becomes computationally expensive on large-scale data sets because of such reasons as the complexity and number of iterations in parameter fitting methods, underlying optimization solvers, and nonlinearity of kernels. We introduce a fast multilevel framew...

Ice breakup forecast in the reach of the Yellow River: the support vector machines approach H. Zhou, W. Li, C. Zhang, and J. Liu School of Civil and Hydraulic Engineering, Dalian University of Technology, Dalian 116024, China Received: 21 March 2009 – Accepted: 23 March 2009 – Published: 9 April 2009 Correspondence to: W. Li ([email protected]) Published by Copernicus Publications on behalf o...

As we saw in the previous lecture, solving this optimization recovers a linear classifier of the form y = sign(w ·h(x)+w0) that minimizes the hinge loss for all misclassified points and maximizes the size of the margin (the distance to the closest point to the decision boundary). The term “support vector” refers to the vectors from the decision boundary to the closest points. Note that moving a...

The computational complexity of solving nonlinear support vector machine (SVM) is prohibitive on large-scale data. In particular, this issue becomes very sensitive when the data represents additional difficulties such as highly imbalanced class sizes. Typically, nonlinear kernels produce significantly higher classification quality to linear kernels but introduce extra kernel and model parameter...

Abstract An algorithm is proposed which generates a nonlinear kernel-based separating surface that requires as little as 1% of a large dataset for its explicit evaluation. To generate this nonlinear surface, the entire dataset is used as a constraint in an optimization problem with very few variables corresponding to the 1% of the data kept. The remainder of the data can be thrown away after so...

Based on the analysis of the conclusions in the statistical learning theory, especially the VC dimension of linear functions, linear programming support vector machines (or SVMs) are presented including linear programming linear and nonlinear SVMs. In linear programming SVMs, in order to improve the speed of the training time, the bound of the VC dimension is loosened properly. Simulation resul...

A widely-used tool for binary classification is the Support Vector Machine (SVM), a supervised learning technique that finds the “maximum margin” linear separator between the two classes. While SVMs have been well studied in the batch (offline) setting, there is considerably less work on the streaming (online) setting, which requires only a single pass over the data using sub-linear space. Exis...

We introduce a semi-supervised support vector machine (S3yM) method. Given a training set of labeled data and a working set of unlabeled data, S3YM constructs a support vector machine using both the training and working sets. We use S3YM to solve the transduction problem using overall risk minimization (ORM) posed by Yapnik. The transduction problem is to estimate the value of a classification ...