一种改善支撑向量域描述性能的核优化算法

An Optimizing Kernel Algorithm for Improving the Performance of Support Vector Domain Description

支撑向量域描述(Support vector domain description,SVDD)是一种重要的数据描述算法,其性能受核参数的影响很大.基于最优核参数应导致特征空间中映射数据的分布是一个超球形区域的思想,提出一种核参数优化算法.首先,基于训练样本在特征空间所张成的子空间的一组标准正交基,给出一种描述映射数据分布的方法,回避了映射数据不可表示的难题;其次,基于最大熵原则的非高斯性测度,构造了一个估计数据分布逼近超球形区域程度的判别准则,用以确定最优核参数.基于仿真数据与实测数据的实验验证了本文方法的有效性。

The support vector domain description （SVDD） is a robust data domain description method. Its performance, however, is strongly influenced by kernel parameter. In this paper, a novel parameter-optimizing algorithm is presented based on the idea that the optimal parameter can lead to the distribution of the mapped data in the feature space to be a hyper-sphere shape. Firstly, based on an orthogonal basis of the subspace spanned by the mapped data, a way is given to capture the structure of the entire mapped data, which avoids the problem that the mapped data cannot be expressed in an explicit form. Secondly, based on the maximum-entropy non-Gaussian measurement, a new criterion is presented for estimating the degree for a distribution to be closes to the hyper-sphere area and it is used to select the suitable kernel parameter. The experiments on simulated data and real-world data demonstrate the effectiveness of the proposed method.