提出了一种基于低密度分割几何距离的半监督KFDA（kernel Fisher discriminant analysis）算法（semisupervised KFDA based on low density separation geometry distance，简称SemiGKFDA）.该算法以低密度分割几何距离作为相似性度量，通过大量无标签样本，提高KFDA算法的泛化能力.首先，利用核函数将原始空间样本数据映射到高维特征空间中；然后，通过有标签样本和无标签样本构建低密度分割几何距离测度上的内蕴结构一致性假设，使其作为正则化项整合到费舍尔判别分析的目标函数中；最后，通过求解最小化目标函数获得最优投影矩阵.人工数据集和UCI数据集上的实验表明，该算法与KFDA及其改进算法相比，在分类性能上有显著提高.此外，将该算法与其他算法应用到人脸识别问题中进行对比，实验结果表明，该算法具有更高的识别精度.

In this study, a novel semi-supervised kernel Fisher discriminant analysis (KFDA) based on low density separation geometric distance is proposed. The method employs the low density separation geometric distance as the measure of similarity and thus improves the generalization ability of the KFDA through a large number of unlabeled samples. First, the original spatial data are implicitly mapped onto the high-dimensional feature space by kernel function. Then, both the labeled data and the unlabeled data are used to capture the consistence assumption of geometrical structure based on low density separation geometric distance, which are incorporated into the objection function of Fisher discriminant analysis as a regularization term. Finally, the optimal projection matrix is obtained by minimizing the objective function. Experiments on artificial datasets and UCI datasets show that the proposed algorithm has a significantly improvement in classification performance compared with the KFDA and its modified approaches. In addition, comparison results with other methods on face recognition problems demonstrate that the proposed algorithm has higher identification accuracy.

TP391

中央高校基本科研业务费专项资金（2572017EB02，2572017CB07）；东北林业大学双一流科研启动基金（411112438）；哈尔滨市科技局创新人才基金（2017RAXXJ018）；国家自然科学基金（31570547）