In this paper, we propose a new algorithm to extend support vector machine (SVM) for binary classification to multicategory classification. The proposed method is based on a sequential binary classification algorithm. We first classify a target class by excluding the possibility of labeling as any other classes using a forward step of sequential SVM; we then exclude the already classified classes and repeat the same procedure for the remaining classes in a backward step. The proposed algorithm relies on SVM for each binary classification and utilizes only feasible data in each step; therefore, the method guarantees convergence and entails light computational burden. We prove Fisher consistency of the proposed forward–backward SVM (FB-SVM) and obtain a stochastic bound for the predicted misclassification rate. We conduct extensive simulations and analyze real-world data to demonstrate the superior performance of FB-SVM, for example, FB-SVM achieves a classification accuracy much higher than the current standard for predicting conversion from mild cognitive impairment to Alzheimer’s disease.

中文翻译：

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通过前向-后向支持向量机进行多类别分类


在本文中，我们提出了一种新算法，将二元分类的支持向量机（SVM）扩展到多类别分类。所提出的方法基于顺序二元分类算法。我们首先通过使用顺序 SVM 的前向步骤排除标记为任何其他类的可能性，对目标类进行分类；然后，我们排除已经分类的类，并向后退一步对剩余的类重复相同的过程。所提出的算法依赖于支持向量机（SVM）进行每个二元分类，并且在每个步骤中仅利用可行的数据；因此，该方法保证收敛并且计算负担轻。我们证明了所提出的前向-后向 SVM (FB-SVM) 的 Fisher 一致性，并获得了预测错误分类率的随机界限。我们进行了广泛的模拟并分析了现实世界的数据，以证明 FB-SVM 的优越性能，例如，FB-SVM 实现的分类精度远高于当前预测从轻度认知障碍到阿尔茨海默病转化的标准。