格拉斯曼流形降维及应用研究

Study on Grassmann Manifold Dimension Reduction and Its Application

视频人脸识别的核心问题是如何准确、高效地构建人脸模型并度量模型的相似性,为此提出一种维数约减的格拉斯曼流形鉴别分析方法以提高集合匹配的性能。首先通过子空间建模图像集合,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,为解决高维矩阵计算开销大以及在小样本条件下不能有效描述样本分布的缺陷,引入二维主成分分析方法对子空间的正交基矩阵降维。通过QR分解正则化降维后的矩阵,得到一个低维、紧致的格拉斯曼流形以获得图像集更好的表达。最后将其投影到高维核空间中进行分类。在公开的视频数据库中的实验结果证明,提出的方法在降低计算开销的同时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 is how to model facial images and measure the similarity between two models.To this end,a dimension reduction method in the Grassmann manifold was proposed to improve the performance of set matching.Firstly,an image set is modeled with a subspace,and the basic element of the Grassmann manifold is presented as the projection matrix by projection mapping.Then,to solve the problem of computational overhead with high dimension matrix,while the model cannot strictly describe the distribution with fewer samples,a two dimensional principal component analysis is implemented to reduce the dimension of the orthogonal basis matrix.By applying QR decomposition on the matrix,a lower dimension and tighten Grassmann manifold is obtained,which can be better to model the image set.Finally,a kernel function that mapped the orthogonal basis matrix from a Grassmann manifold to Euclidean space is used to classify image sets.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,and it outperforms other state of the art set-based matching methods with lower computational cost.