基于近似零范数的稀疏核主成成分算法

Sparse kernel principal component algorithm based on an approximate zero norm

核主成成分分析(KPCA)是一种有效的数据降维方法,其降维过程是计算待降维样本与所有训练样本核函数的线性叠加,所以其计算量依赖于训练样本的大小,致使降维效率很低。为了提高KPCA降维效率,提出利用近似的零范数对叠加系数施加稀疏约束,能够得到稀疏性很好的系数。降维时,去除大量系数为零的训练样本,所以能够显著提高降维速度。通过实验还发现该算法对离群点具有不错的鲁棒性,换句话说当训练人脸数据库中加入非人脸图像时能够较好的克服这些非人脸图像的影响。

Kernel principal component analysis （KPCA） is an effective method for data dimension reduction. The process is a linear superposition of samples for dimension reduction and kernel function of train samples, so the computation depends on the size of train samples, thus leading a lower efficiency. In order to improve efficiency of KPCA,this paper proposes applying a sparse constraint by an approximate zero norms to superposition coefficients,and obtains good sparse coefficients. When reducing dimensions, many train samples whose coefficient is zero are rejected, thus significant improving speed of dimension reduction. We also find this technique shows strong robustness for outliers by experiments, in other words, the algorithm proposed can overcome influence when we join non-face images to train face database.