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图学学报

• 视觉与图像 • 上一篇    下一篇

低维格拉斯曼流形鉴别分析

  

  1. 广州番禺职业技术学院信息工程学院，广东广州 511483
  • 出版日期:2017-02-28 发布日期:2017-02-22
  • 基金资助:
    广东省自然科学基金项目(2015A030313807)；广州市属高校科研项目(1201610059)；广州市教育系统创新团队建设计划(1201610034)；广
    州番禺职业技术学院“十三五”科研项目(2016X002)；广东省高等职业教育教学改革项目(201401181)

Low Dimension Discriminant Analysis on Grassmann Manifold

  1. School of Information and Technology, Guangzhou Panyu Polytechnic, Guangzhou Guangdong 511483, China
  • Online:2017-02-28 Published:2017-02-22

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摘要： 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。

关键词: 子空间, 集合匹配, 格拉斯曼流形, 投影度量, 度量学习

Abstract: 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.

Key words: subspace, set matching, Grassmann manifold, projection metric, metric learning