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      Gradient Algorithm on Stiefel Manifold and Application in Feature Extraction

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          Abstract

          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.

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          Author and article information

          Journal
          Journal of Radars
          Chinese Academy of Sciences
          01 September 2013
          : 2
          : 3
          : 309-313
          Affiliations
          [1 ] College of Electronic and Information Engineering, Nanjing University of Aeronautics and Astronautics
          [2 ] Unmanned Aerial Vehicle Research Department, Nanjing University of Aeronautics and Astronautics
          Article
          cf9998affb26407d921628564a216e7c
          10.3724/SP.J.1300.2013.13048

          This work is licensed under a Creative Commons Attribution 4.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

          Categories
          Technology (General)
          T1-995

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