中文摘要：

以协方差鉴别学习（covariance discriminative learning，CDL）为基础，对图像集的隶属于黎曼流形之上的协方差矩阵进行双向降维。将降维后的协方差矩阵与有效的黎曼度量，如对数欧氏距离（log euclidean distance， LED）结合得到一个核函数来将这些协方差矩阵映射到欧式空间中进行分类。改进的CDL方法由于减少了协方差矩阵的维数，从而降低了计算复杂度并提高了分类精度。通过在标准数据集上的实验，验证了该改进方法的有效性。

英文摘要：

Based on the original Covariance Discriminative Learning method,a bidirectional dimension reduction was applied on those covariance matrices,which lied on a Riemannian manifold.Combining these covariance matrices with an efficient Riemannian metric,i.e.,log euclidean distance （LED）,a kernel function that mapped the covariance ma-trix from Riemannian manifold to Euclidean space for classification was derived.As a result of dimension reduction of covariance matrices,this method improved accuracy of classification and reduced the complexity of computation.The results were observed through experiments on standard datasets.