A generalized minor component extraction algorithm and its convergence analysis

DU Bo-yang1 KONG Xiang-yu1 FENG Xiao-wei1 GAO Ying-bin1 LUO Jia-yu1

(1.College of Missile Engineering, The Rocket Force University of Engineering, Xi’an, Shaanxi Province, China 710025)

【Abstract】Generalized minor component analysis (GMCA) has played a vital role in many areas of modern signal processing. Up to now, few algorithms can possess four properties together, which are the information criterion corresponding to the algorithm, convergence, self-stabilizing, and ability of extracting multiple generalized minor components (GMCs). To deal with this problem, a novel information criterion is proposed and based on the criterion, an algorithm for GMCs extraction is derived. Then, the global convergence of the algorithm is analyzed with the deterministic discrete time method. Besides, self-stability is illustrated through theoretical research on the relationship between the convergence ability and the initial state of the algorithm. Furthermore, the application of the algorithm in multiple GMCs extraction is employed. In contrast with the existing algorithms, the proposed algorithm is the best of its kind in convergence speed. The properties of the algorithm are verified through MATLAB simulation.

【Keywords】 generalized minor component analysis (GMCA); deterministic discrete time (DDT); convergence analysis; self-stabilizing property;


【Funds】 National Natural Science Foundation of China (61374120, 61673387)

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This Article


CN: 21-1124/TP

Vol 35, No. 06, Pages 1505-1511

June 2020


Article Outline



  • 0 Introduction
  • 1 The proposed algorithm
  • 2 Self-stability of the proposed algorithm
  • 3 Convergence analysis of the proposed algorithm
  • 4 Multiple GMCs extraction
  • 5 Simulation examples
  • 6 Conclusions
  • References