带高斯核的支持向量数据描述问题的高效积极集法  

Efficient active-set method for support vector data description problem with Gaussian kernel

作　　者：张奇业[1] 曾心蕊 ZHANG Qiye;ZENG Xinrui(School of Mathematical Sciences,Beihang University,Beijing 102206,China)

机构地区：[1]北京航空航天大学数学科学学院,北京102206

出　　处：《计算机应用》2024年第12期3808-3814,共7页journal of Computer Applications

基　　金：北京航空航天大学研究生教育与发展研究专项基金资助项目(JG2023014)。

摘　　要：针对积极集法求解支持向量数据描述(SVDD)问题时,在大规模数据场景下每次迭代计算量大、效率低的问题,设计一种带高斯核的SVDD问题的高效积极集法(ASM-SVDD)。首先,利用SVDD对偶模型约束条件的特殊性,每次迭代求解一个降维的等式约束子问题;其次,通过矩阵操作实现积极集的更新,每次更新计算只与当前支持向量及单个样本点有关,从而极大地降低计算量;另外,由于ASM-SVDD算法是传统积极集法的一种变体,应用积极集法理论得到该算法的有限终止性;最后,基于仿真和真实数据集,验证ASM-SVDD算法性能。结果表明,随着训练轮次的增加,ASM-SVDD算法可以有效提升模型性能。与求解SVDD问题的快速增量算法FISVDD (Fast Incremental SVDD)相比,ASM-SVDD算法在典型的低维高样本数据集shuttle上训练得到的目标函数值可减小25.9%,对支持向量的识别能力可提高10.0%。同时,ASM-SVDD算法在不同数据集上的F1分数相较于FISVDD算法均有提高,在超大规模数据集criteo上提高量可达0.07%。可见,ASM-SVDD算法在检测异常值的同时,训练得到的超球体更稳定,且对测试样本的判断准确率也更高,适用于大规模数据场景下的异常值检测。To address the large amount of calculation and low efficiency during each iteration in large-scale data scenarios when using active-set method to solve the problem of Support Vector Data Description(SVDD),an efficient Active-Set Method for SVDD problem with Gaussian kernel(ASM-SVDD)was designed.Firstly,due to the peculiarity of constraint conditions in SVDD dual model,a dimension-reduced subproblem with equality constraints was solved in each iteration.Then,the active-set was updated through matrix manipulations.Each update calculation was only related to the existing support vectors and a single sample point,which reduced the amount of computation dramatically.In addition,since ASM-SVDD algorithm can be seen as a variant of the traditional active-set method,the limited termination of this algorithm was obtained by applying the theory of active-set method.Finally,simulation and real datasets were used to verify the performance of ASM-SVDD algorithm.The results show that ASM-SVDD algorithm can improve the model performance effectively as the number of training rounds increases.Compared to the fast incremental algorithm to solve SVDD problem—FISVDD(Fast Incremental SVDD),ASM-SVDD algorithm has the objective value obtained by training reduced by 25.9%and the recognition ability of support vectors improved by 10.0%on the typical low-dimensional high-sample dataset shuttle.At the same time,ASM-SVDD algorithm obtains F1 scores on different datasets all higher than FISVDD algorithm with the maximum improvement of 0.07%on the super large-scale dataset criteo.It can be seen that ASM-SVDD algorithm can obtain more stable hypersphere through training,and obtain higher judgment accuracy of test samples while performing outlier detection.Therefore,ASM-SVDD algorithm is suitable for outlier detection in large-scale data scenarios.

关 键 词：支持向量数据描述 二次规划 积极集法 异常值检测 有限终止性 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构]