Abstract: Maximum Variance Difference Embedding（VDE） maximizes the difference between the global variance and the local variance, which utilizes the maximum variance difference criterion rather than the generalized Rayleigh quotient criterion as a class separability measure, thereby avoiding the singularity problem of Unsupervised Discriminant Projection（UDP） when addressing the sample size problem. However, VDE is a linear approach, which cannot describe the complex nonlinear data, such as biometric data. To enhance the nonlinear description ability of VDE, it can optimize the objective function of VDE in reproducing kernel Hilbert space to construct Kernel-based maximum Variance Difference Embedding（KVDE） approach. Compared with some other related classical methods, experimental results on face and palmprint recognition problems indicate the effectiveness of the proposed KVDE.

Key words: global variance, local variance, kernel maximum variance difference embedding, biometric feature extraction

摘要： 最大方差差分嵌入算法（VDE）最大化全局方差和局部方差之差，该算法直接通过求解一个特征值问题而获得投影矩阵，无需矩阵求逆运算，因此VDE克服了无监督鉴别投影（UDP）算法的小样本问题，为了进一步增强VDE算法的非线性描述能力，提出了核最大方差差分嵌入算法（KVDE），该算法首先采用核函数将样本映射到非线性高维空间，然后采用核方法得到一个低维子空间，人脸和掌纹数据库上的实验表明KVDE算法比VDE算法具有更好的性能。

关键词: 全局方差, 局部方差, 核最大方差差分嵌入, 生物特征提取