Chen Huakun, Lyu Yongxi, Shi Jingping, Zhang Weiguo
Department of Automatic Control, Northwestern Polytechnical University, Xi'an 710072, China.
Entropy (Basel). 2024 Jul 25;26(8):628. doi: 10.3390/e26080628.
Support vector data description (SVDD) is widely regarded as an effective technique for addressing anomaly detection problems. However, its performance can significantly deteriorate when the training data are affected by outliers or mislabeled observations. This study introduces a universal truncated loss function framework into the SVDD model to enhance its robustness and employs the fast alternating direction method of multipliers (ADMM) algorithm to solve various truncated loss functions. Moreover, the convergence of the fast ADMM algorithm is analyzed theoretically. Within this framework, we developed the truncated generalized ramp, truncated binary cross entropy, and truncated linear exponential loss functions for SVDD. We conducted extensive experiments on synthetic and real-world datasets to validate the effectiveness of these three SVDD models in handling data with different noise levels, demonstrating their superior robustness and generalization capabilities compared to other SVDD models.
支持向量数据描述（SVDD）被广泛认为是解决异常检测问题的有效技术。然而，当训练数据受到异常值或错误标记观测值的影响时，其性能可能会显著下降。本研究将通用截断损失函数框架引入SVDD模型以增强其鲁棒性，并采用快速交替方向乘子法（ADMM）算法来求解各种截断损失函数。此外，从理论上分析了快速ADMM算法的收敛性。在此框架内，我们为SVDD开发了截断广义斜坡、截断二元交叉熵和截断线性指数损失函数。我们在合成数据集和真实世界数据集上进行了广泛的实验，以验证这三种SVDD模型在处理不同噪声水平数据方面的有效性，证明它们与其他SVDD模型相比具有卓越的鲁棒性和泛化能力。
