低维格拉斯曼流形鉴别分析

Low Dimension Discriminant Analysis on Grassmann Manifold

图像集匹配需要解决如何对集合模型并度量模型之间的相似性的问题,为此提出一种维数约减的格拉斯曼流形鉴别分析方法并用于对象和人脸识别。首先引入投影映射将格拉斯曼流形上的基本元素表示成对应的投影矩阵。然后,为克服高维矩阵在小样本条件下不能有效描述样本分布的缺陷,通过投影度量学习对子空间的正交基矩阵降维得到一个低维、紧致的格拉斯曼流形以获得图像集更好地表达。最后投影到再生核希尔伯特空间中进行分类。在公开的视频数据库中的实验结果证明,该方法能够获得较高的正确率,是一种有效的基于集合的对象匹配和人脸识别方法。

The key issues of video based face recognition are the way to model facial images precision and high efficiency and measure the similarity between two sets. To end this, a Grassmann manifold dimension reduction method is proposed to improve the performance of image set matching. Firstly, a subspace constructed by an image set is presented as a point in a Grassmann manifold with a projection matrix. Then, a projection metric learning approach is applied to reduce the dimension of the orthogonal basis matrix to obtain a lower dimension and tighten Grassmann manifold. Finally, a kernel function mapped the orthogonal basis matrix from a Grassmann manifold to Euclidean space for classification. Extensive experimental results on shared video based dataset show that the proposed method is an effective object matching and face recognition method based on set-to-set matching.