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    最大向量夹角间隔核分类

    Maximum Vector-Angular Margin Kernel Classification

    • 摘要: 提出了一种最大向量夹角间隔MAMC分类方法,其核心思想是在样本特征空间中寻找一个尽可能靠近训练样本中心的向量c,进而强化更小的VC维,同时未知样本点可以根据向量c和训练样本点之间的最大向量夹角间隔ρ进行分类.提出的MAMC方法可以通过核化提高算法的灵活性,而在MAMC方法的实现上,只需解决一个对应的二次凸优化问题,实现简单.同时,MAMC的v×v\-1参数属性构成了支持向量个数的下界和错分训练样本数的上界;而其所对应的硬划分版本可以等价于一种特殊和核化的最小包含球,因此能够训练较大样本.最后,人造和真实数据集实验结果表明,MAMC整体上具有较好的性能优势.

       

      Abstract: A maximum vector-angular margin classification mechanism, called MAMC, is proposed in this paper. Its core idea is to find a vector c in patterns feature space, which is as close as possible to the center of the training samples for the smaller VC dimension, such that all the data points can be classified in terms of the maximum vector-angular margin ρ between the vector c and all the training points. The proposed approach MAMC can not only be kernelized to enhance its flexibility, but also be simply realized by solving a corresponding convex optimization problem. Furthermore, its v×v\-1 parameter property is respectively the lower bound of support vectors and the upper bound of misclassified patterns, which is similar to the v-SVC algorithm. Meanwhile, the corresponding hard margin version can be equivalently formulated as a special and kernelized minimum enclosing ball (MEB), called the center constraint MEB (CC-MEB), thus the MAMC may be extended to another version for training on large datasets by using generalized core vector machine (CVM). Experimental results about artificial and real datasets illustrate that the obtained effectiveness of the proposed method is competitive.

       

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