基于测地Gabriel图的非线性流形判别分析

针对位于非线性流形上类别数据的判别分析问题,提出了一种基于测地Gabriel图的局部判别器融合算法.利用测地距离表征流形的内在几何结构,由此构造测地Gabriel图确定异类数据相互靠近的局部临界区域,进而训练得到局部线性的判别器.整体的非线性判别器由多个局部判别器融合得到:基于柔性边界准则函数,以迭代优化的方式,为每个局部判别器分配最佳的权重系数,整体上逐步提高异类样本间的区分度.在人工合成数据集以及人脸图像库上的实验证明了本文算法的有效性.

Discriminant Analysis on Nonlinear Manifold Based on Geodesic Gabriel Graph

As for the discriminant analysis on nonlinear manifold, a geodesic Gabriel graph based local discriminant merging approach was proposed. Using geodesic distance to discover the intrinsic geometry of the manifold,the geodesic Gabriel graph was constructed to locate the critical local regions where the local linear discriminants would be learned. The global nonlinear discriminant was achieved by merging the multiple local discriminants. The soft margin criterion based merging algorithm assigned the best weight to each local discriminant in an iterative way and upgraded the detection accuracy stepwise. The superiority of this algorithm was confirmed by experiments both on synthesized data and face image set.