Abstract: A novel kernel-projection non-negative matrix factorization algorithm is proposed to improve the poor convergence of the traditional non-negative matrix factorization for the higher sample dimension in this study. The kernel matrix, characterizing the similarity of the samples, is achieved by the kernel projection to decrease samples’ within-class scatter and increase the between-class scatter, which can suppress the interior noise and improve linear separability of the samples. The kernel projection matrix is decomposed into basis vectors and weight coefficient matrix with the non-negative constraint. The weight coefficient matrix as the original samples characteristics is utilized for the image analysis. Face image feature extraction and classification experiments show that the proposed algorithm can extract the features better and improve the classification accuracy.

Key words: kernel projection matrix, non-negative factorization, face image, feature extraction

摘要： 针对非负矩阵分解算法在样本维数过高情况下收敛效果差的问题，提出了一种核矩阵非负分解算法。通过核映射方法获得表征样本间相似度的核矩阵，以减小样本类内散度，增大样本类间散度，从而改善样本内部噪声干扰，提高样本间的线性可分度；再将核矩阵在非负条件约束下分解为基向量及其加权系数矩阵，用系数矩阵作为原样本特征。经人脸图像特征提取与分类实验验证，新算法可更好地提取高维人脸图像的低维特征，提高分类正确率。

关键词: 核矩阵, 非负分解, 人脸图像, 特征提取