一种广义次成分提取算法及其收敛性分析

广义次成分分析(generalized minor component analysis, GMCA)在现代信号处理的许多领域具有重要作用.目前现有的大多算法不能同时具备与算法对应的信息准则,以及收敛性、自稳定性和多个广义次成分提取的性能.针对上述问题,利用一种新的信息传播规则,推导出一种广义次成分提取算法,并采用确定离散时间方法(deterministic discrete time, DDT)对算法的全局收敛性能进行分析;同时,通过理论分析算法的收敛性能与算法初始状态的关系,表明算法具有自稳定性.进一步地,探索了算法在多重广义次成分提取方面的应用.相比之前的算法,所提算法具有更快的收敛速度. Matlab仿真验证了所提出算法的各项性能.

A generalized minor component extraction algorithm and its convergence analysis

Generalized minor component analysis(GMCA) has played a vital role in many areas of the modern signal processing. Up to now, few algorithms can possess four properties together, which are the information criterion corresponding to the algorithm, convergence property, self-stabilizing property and ability of extracting multiple generalized minor components. To deal with this problem, a novel information criterion is proposed and based on the criterion, a generalized minor component extraction algorithm is derived. Then, the global convergence of the algorithm is analyzed using the deterministic discrete time method. Besides, self-stabilizing property is illustrated through theorical researching on the relationship between the convergence ability and initial state of the algorithm. Furthermore, the application of the algorithm in multiple GMCs extraction is exploved. In contrast with the existing algorithms, the proposed algorithm is superior in convergence speed. The properties of the algorithm are verified by simulations in Matlab.