Extending twin support vector machine classifier for multi-category classification problems

© 2013 – IOS Press and the authors. All rights reservedTwin support vector machine classifier (TWSVM) was proposed by Jayadeva et al., which was used for binary classification problems. TWSVM not only overcomes the difficulties in handling the problem of exemplar unbalance in binary classification problems, but also it is four times faster in training a classifier than classical support vector machines. This paper proposes one-versus-all twin support vector machine classifiers (OVA-TWSVM) for multi-category classification problems by utilizing the strengths of TWSVM. OVA-TWSVM extends TWSVM to solve k-category classification problems by developing k TWSVM where in the ith TWSVM, we only solve the Quadratic Programming Problems (QPPs) for the ith class, and get the ith nonparallel hyperplane corresponding to the ith class data. OVA-TWSVM uses the well known one-versus-all (OVA) approach to construct a corresponding twin support vector machine classifier. We analyze the efficiency of the OVA-TWSVM theoretically, and perform experiments to test its efficiency on both synthetic data sets and several benchmark data sets from the UCI machine learning repository. Both the theoretical analysis and experimental results demonstrate that OVA-TWSVM can outperform the traditional OVA-SVMs classifier. Further experimental comparisons with other multiclass classifiers demonstrated that comparable performance could be achieved.This work is supported in part by the grant of the Fundamental Research Funds for the Central Universities of GK201102007 in PR China, and is also supported by Natural Science Basis Research Plan in Shaanxi Province of China (Program No.2010JM3004), and is at the same time supported by Chinese Academy of Sciences under the Innovative Group Overseas Partnership Grant as well as Natural Science Foundation of China Major International Joint Research Project (NO.71110107026)

Fuzzy Least Squares Twin Support Vector Machines

Least Squares Twin Support Vector Machine (LST-SVM) has been shown to be an efficient and fast algorithm for binary classification. It combines the operating principles of Least Squares SVM (LS-SVM) and Twin SVM (T-SVM); it constructs two non-parallel hyperplanes (as in T-SVM) by solving two systems of linear equations (as in LS-SVM). Despite its efficiency, LST-SVM is still unable to cope with two features of real-world problems. First, in many real-world applications, labels of samples are not deterministic; they come naturally with their associated membership degrees. Second, samples in real-world applications may not be equally important and their importance degrees affect the classification. In this paper, we propose Fuzzy LST-SVM (FLST-SVM) to deal with these two characteristics of real-world data. Two models are introduced for FLST-SVM: the first model builds up crisp hyperplanes using training samples and their corresponding membership degrees. The second model, on the other hand, constructs fuzzy hyperplanes using training samples and their membership degrees. Numerical evaluation of the proposed method with synthetic and real datasets demonstrate significant improvement in the classification accuracy of FLST-SVM when compared to well-known existing versions of SVM

High-performance Kernel Machines with Implicit Distributed Optimization and Randomization

In order to fully utilize "big data", it is often required to use "big models". Such models tend to grow with the complexity and size of the training data, and do not make strong parametric assumptions upfront on the nature of the underlying statistical dependencies. Kernel methods fit this need well, as they constitute a versatile and principled statistical methodology for solving a wide range of non-parametric modelling problems. However, their high computational costs (in storage and time) pose a significant barrier to their widespread adoption in big data applications. We propose an algorithmic framework and high-performance implementation for massive-scale training of kernel-based statistical models, based on combining two key technical ingredients: (i) distributed general purpose convex optimization, and (ii) the use of randomization to improve the scalability of kernel methods. Our approach is based on a block-splitting variant of the Alternating Directions Method of Multipliers, carefully reconfigured to handle very large random feature matrices, while exploiting hybrid parallelism typically found in modern clusters of multicore machines. Our implementation supports a variety of statistical learning tasks by enabling several loss functions, regularization schemes, kernels, and layers of randomized approximations for both dense and sparse datasets, in a highly extensible framework. We evaluate the ability of our framework to learn models on data from applications, and provide a comparison against existing sequential and parallel libraries.Comment: Work presented at MMDS 2014 (June 2014) and JSM 201