Two-Layer SVM, Towards Deep Statistical Learning

Alireza Kazemi, R. Boostani, Mahmoud Odeh, M. Al-Mousa
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Abstract

Support Vector Machine (SVM) is originally a binary large-margin classifier emerged from the concept of structural risk minimization. Multiple solutions such as one-versus-one and one-versus-all have been proposed for creating multi-class SVM using elementary binary SVMs. Also multiple solutions have been proposed for SVM model selection, adjusting margin-parameter C and the Gaussian kernel variance. Here, an improved classifier named SVM-SVM is proposed for multi-class problems which increases accuracy and decreases dependency to margin-parameter selection. SVM-SVM adopts two K-class one-vs-one SVMs in a cascaded two-layer structure. In the first layer, input features are fed to one-vs-one SVM with non-linear kernels. We introduce this layer as a large-margin non-linear feature transform that maps input feature space to a discriminative K*(K-1)/2 dimensional space. To assess our hierarchical classifier, some datasets from the UCI repository are evaluated. Standard one-vs-one SVM and one-vs-one fuzzy SVM are used as reference classifiers in experiments. Results show significant improvements of our proposed method in terms of test accuracy and robustness to the model (margin and kernel) parameters in comparison with the reference classifiers. Our observations suggest that a multi-layer (deep) SVM structures can gain the same benefits as is seen in the deep neural nets (DNNs).
面向深度统计学习的两层SVM
支持向量机(SVM)最初是一种基于结构风险最小化概念的二值大余量分类器。针对利用初等二值支持向量机创建多类支持向量机,提出了一对一、一对全等多种解决方案。对于支持向量机模型的选择、边缘参数C的调整和高斯核方差的调整也提出了多种解决方案。针对多类问题,提出了一种改进的SVM-SVM分类器,提高了分类准确率,减少了对边缘参数选择的依赖。SVM-SVM采用两个k类1对1支持向量机,在级联的两层结构中。在第一层,输入特征被馈送到具有非线性核的一对一支持向量机。我们将这一层作为大边界非线性特征变换引入,将输入特征空间映射到判别性的K*(K-1)/2维空间。为了评估我们的分层分类器,我们评估了来自UCI存储库的一些数据集。实验采用标准的一对一支持向量机和一对一模糊支持向量机作为参考分类器。结果表明,与参考分类器相比,我们提出的方法在测试精度和对模型(边际和核)参数的鲁棒性方面有显著改进。我们的观察表明,多层(深度)支持向量机结构可以获得与深度神经网络(dnn)相同的好处。
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