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摘要: 并行主成分提取算法在信号特征提取中具有十分重要的作用, 采用加权规则将主子空间(Principal subspace, PS)提取算法转变为并行主成分提取算法是很有效的方式, 但研究加权规则对状态矩阵影响的理论分析非常少. 对加权规则影响的分析不仅可以提供加权规则下的主成分提取算法动力学的详细认知, 而且对于其他子空间跟踪算法转变为并行主成分提取算法的可实现性给出判断条件. 本文通过比较Oja的主子空间跟踪算法和加权Oja并行主成分提取算法, 通过两种算法的差异分析了加权规则对算法提取矩阵方向的影响. 首先, 针对二维输入信号, 研究了提取两个主成分时加权规则的信息准则对状态矩阵方向的作用方式. 进而, 针对大于二维输入信号的情况, 给出加权规则影响多个主成分提取方式的讨论. 最后, MATLAB仿真验证了所提出理论的有效性.Abstract: The parallel principal component extraction algorithms play an important role in signal feature extraction. It is very effective and very useful to modify the principal subspace (PS) extraction algorithms into parallel principal components extraction algorithms by using weighted rules, but so far, few people theoretically analyze the variation of the state matrix under the extraction algorithm of weighted rules. The analysis of this variation can not only provide detailed knowledge of the dynamics of the principal component extraction algorithms under weighted rules, but also give the realization conditions for transferring subspace extraction algorithms into parallel principal components extraction algorithm. In this paper, by comparing the difference between Oja principal subspace extraction algorithm and weighted Oja parallel principal components extraction algorithm, the influence of weighted rules on the extraction direction is analyzed. Firstly, for the case of extracting two principal components, the influence of the information criterion under the weighted rule on the direction of the state matrix is studied. Furthermore, for the case of extracting more than two principal components, a discussion is given on the manner where the weighted rules are applied. Finally, the MATLAB simulation verifies the validity of the proposed theory.
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图 1 Oja信息准则和加权Oja信息准则在
$\theta$ 变化情况下的数值变化Fig. 1 Curves of the information criterion Oja and weighted Oja algorithms on
$\theta$ 
图 2 Oja信息准则和加权Oja信息准则在
$\theta = \dfrac{\pi}{2}$ 处的投影Fig. 2 Projection of the information criterion Oja and weighted Oja algorithms when
$\theta = \dfrac{\pi}{2}$ 
图 4 加权Oja信息准则在
$\theta$ 变化情况下的数值变化Fig. 4 Curves of weighted Oja information criterion on
$\theta$ 
图 5 Miao信息准则和Ouyang信息准则在
$\theta$ 变化情况下的数值变化Fig. 5 Curves of the information criterion Miao and Ouyang algorithms on
$\theta$ 
图 6 Miao信息准则和Ouyang信息准则在
$\theta = \dfrac{\pi}{2}$ 处的投影Fig. 6 Projection of the information criterion Miao and Ouyang algorithms when
$\theta = \dfrac{\pi}{2}$ 
图 7 Miao信息准则在
$\theta$ 变化情况下的数值变化Fig. 7 Curves of Miao information criterion on
$\theta$ 
图 8 Ouyang信息准则在
$\theta$ 变化情况下的数值变化Fig. 8 Curves of Ouyang information criterion on
$\theta$ -
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