Volume 2 Issue 3
Sep.  2013
Turn off MathJax
Article Contents
Zhang Jian-jun, Cao Jie, Wang Yuan-yuan. Gradient Algorithm on Stiefel Manifold and Application in Feature Extraction[J]. Journal of Radars, 2013, 2(3): 309-313. doi: 10.3724/SP.J.1300.2013.13048
Citation: Zhang Jian-jun, Cao Jie, Wang Yuan-yuan. Gradient Algorithm on Stiefel Manifold and Application in Feature Extraction[J]. Journal of Radars, 2013, 2(3): 309-313. doi: 10.3724/SP.J.1300.2013.13048

Gradient Algorithm on Stiefel Manifold and Application in Feature Extraction

doi: 10.3724/SP.J.1300.2013.13048
  • Received Date: 2013-05-22
  • Rev Recd Date: 2013-08-30
  • Publish Date: 2013-06-28
  • To improve the computational efficiency of system feature extraction, reduce the occupied memory space, and simplify the program design, a modified gradient descent method on Stiefel manifold is proposed based on the optimization algorithm of geometry frame on the Riemann manifold. Different geodesic calculation formulas are used for different scenarios. A polynomial is also used to lie close to the geodesic equations. JiuZhaoQin-Horner polynomial algorithm and the strategies of line-searching technique and change of the step size of iteration are also adopted. The gradient descent algorithm on Stiefel manifold applied in Principal Component Analysis (PCA) is discussed in detail as an example of system feature extraction. Theoretical analysis and simulation experiments show that the new method can achieve superior performance in both the convergence rate and calculation efficiency while ensuring the unitary column orthogonality. In addition, it is easier to implement by software or hardware.

     

  • loading
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索
    Article views(3229) PDF downloads(3189) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint