论文标题
$ \ ell_p $ slack norm支持向量数据描述
$\ell_p$ Slack Norm Support Vector Data Description
论文作者
论文摘要
支持矢量数据描述（SVDD）方法是一级分类的事实上的标准，其中学习任务需要推断最小的超音速以封闭目标对象，同时通过$ \ ell_1 $ norm-norm惩罚性惩罚任何错误/休闲。在这项研究中，我们将这种建模形式主义推广到一般的$ \ ell_p $ -norm（$ p \ geq1 $）松弛惩罚函数。借助$ \ ell_p $ slack norm，该建议的方法可实现相对于休闲仪的非线性成本函数。从双重问题的角度来看，所提出的方法将引起稀疏性双重规范引入目标函数，因此具有更高的能力，可以调整问题的固有稀疏性，以增强描述能力。基于Rademacher复杂性的理论分析以参数$ p $为角度表征了所提出方法的概括性能，而几个数据集的实验结果与其他替代方案相比确认了该方法的优点。
The support vector data description (SVDD) approach serves as a de facto standard for one-class classification where the learning task entails inferring the smallest hyper-sphere to enclose target objects while linearly penalising any errors/slacks via an $\ell_1$-norm penalty term. In this study, we generalise this modelling formalism to a general $\ell_p$-norm ($p\geq1$) slack penalty function. By virtue of an $\ell_p$ slack norm, the proposed approach enables formulating a non-linear cost function with respect to slacks. From a dual problem perspective, the proposed method introduces a sparsity-inducing dual norm into the objective function, and thus, possesses a higher capacity to tune into the inherent sparsity of the problem for enhanced descriptive capability. A theoretical analysis based on Rademacher complexities characterises the generalisation performance of the proposed approach in terms of parameter $p$ while the experimental results on several datasets confirm the merits of the proposed method compared to other alternatives.
