As a state-of-the-art multi-class supervised novelty detection method, supervised novelty detection-support vector machine (SND-SVM) is extended from one-class support vector machine (OC-SVM). It still requires to slove a more time-consuming quadratic programming (QP) whose scale is the number of training samples multiplied by the number of normal classes. In order to speed up SND-SVM learning, we propose a down sampling framework for SND-SVM. First, the learning result of SND-SVM is only decided by minor samples that have non-zero Lagrange multipliers. We point out that the potential samples with non-zero Lagrange multipliers are located in the boundary regions of each class. Second, the samples located in boundary regions can be found by a boundary detector. Therefore, any boundary detector can be incorporated into the proposed down sampling framework for SND-SVM. In this paper, we use a classical boundary detector, local outlier factor (LOF), to illustrate the effective of our down sampling framework for SND-SVM. The experiments, conducted on several benchmark datasets and synthetic datasets, show that it becomes much faster to train SND-SVM after down sampling.

作为一种最新的多类有监督新颖性检测方法，有监督新颖性检测支持向量机（SND-SVM）从一类支持向量机（OC-SVM）扩展而来。仍然需要取消耗时的二次编程（QP），其规模是训练样本数乘以正常类别数。为了加快SND-SVM的学习速度，我们提出了SND-SVM的下采样框架。首先，SND-SVM的学习结果仅由具有非零拉格朗日乘数的次要样本决定。我们指出，具有非零拉格朗日乘数的潜在样本位于每个类别的边界区域中。其次，可以通过边界检测器找到位于边界区域中的样本。因此，可以将任何边界检测器并入为SND-SVM建议的下采样框架。在本文中，我们使用经典边界检测器局部离群值因子（LOF）来说明我们的SND-SVM下采样框架的有效性。在几个基准数据集和综合数据集上进行的实验表明，降采样后训练SND-SVM变得更快。