混合指数损失下的鲁棒一分类支持向量机

Robust One-Class Support Vector Machine under Hybrid Exponential Loss

摘要: 支持向量数据描述(SVDD, Support Vector Data Description)凭借其在单分类和异常检测任务执行中的优异表现，受到了广泛关注。然而，若在建模过程中为所有松弛变量直接分配相同权重，当训练数据混入部分异常值或标签标注错误的观测数据时，模型的学习性能便有可能出现下降。为此，本文提出一种扩展型SVDD模型，通过混合指数损失函数对SVDD原本的优化问题进行重新构建。该损失函数能够突出更有可能归属于目标类的样本的重要性，同时削弱更易成为异常值的样本所产生的影响，因此这一模型也可被视作加权型SVDD。但与传统加权方式不同的是，新模型中的权重为自动计算所得，并非通过特定方法预先计算。为有效求解所提模型的优化问题，本文采用半二次优化技术开展优化计算，进而构建出一种动态优化算法。同时，本文还从理论角度分析了该动态优化算法的收敛性与计算复杂度。此外，本文还展示了在合成数据集及多个公开真实数据集上取得的实验结果，以此验证该新方法相较于传统SVDD及其他同类SVDD改进模型的性能优势。

Abstract: Support Vector Data Description (SVDD) has attracted extensive attention due to its excellent performance in performing one-class classification and anomaly detection tasks. However, if the same weight is directly assigned to all slack variables during the modeling process, the learning performance of the model may decline when the training data is contaminated with some outliers or observation data with mislabeled tags. For this reason, this paper proposes an extended SVDD model by reformulating the original optimization problem of SVDD with a mixed exponential loss function. This loss function can highlight the importance of samples that are more likely to belong to the target class and attenuate the effects of samples that are more prone to being outliers, so this model can also be regarded as a weighted SVDD. Unlike traditional weighting methods, however, the weights in the new model are calculated automatically and not precomputed by a specific method. To effectively solve the optimization problem of the proposed model, a semi-quadratic optimization technique is adopted for optimization calculation in this paper, thereby constructing a dynamic optimization algorithm. Meanwhile, this paper analyzes the convergence and computational complexity of this dynamic optimization algorithm from a theoretical perspective. In addition, this paper presents the experimental results obtained on synthetic datasets and several public real datasets to verify the performance advantages of the new method compared with the traditional SVDD and other competing improved SVDD models.