LS-SVM的非线性特征提取新方法及与PCA的关系研究

Nonlinear Feature Extraction Method Using LS-SVM and its Relation with PCA

提出一种基于最小二乘支持向量机(LS-SVM)的非线性特征提取新方法.先将线性特征提取公式表达成与LS-SVM回归算法中相同的形式;再根据SVM思想,将数据集由输入空间映射到高维特征空间,进而通过核技巧实现非线性特征提取.在理论上证明了所提特征提取方法的结果与PCA方法具有一致性,是传统PCA的一种对偶形式,更适合高维特征数据集的提取.最后,通过近红外光谱数据集特征提取实例验证了在上述条件下该方法的优越性.

A new nonlinear feature extraction method based on least squares support vector machine （LS-SVM） was presented. Firstly, the formulation of linear feature extraction was made in the same fashion as that in the LS-SVM linear regression algorithm. Then the data was mapped from the original input space to a high dimensional feature by following the usual SVM methodology and nonlinear feature extraction could be obtained from linear version of the formulation through applying the kernel trick. It was proved that the presented method, for which the solution coincided with PCA, was a dual problem of the later. So it is suitable for feature extraction in higher-dimensional dataset. Experiment results of near-infrared（NIR） spectrometry feature extraction demonstrate its superior performance in the conditions.