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摘要: 提出一套针对加权Möller算法的广义加权规则用于探讨改进并行提取次成分分析的理论和方法问题.该规则仅在加权Möller算法上引入一个加权规则参数, 通过调节参数后算法性能上的变化, 实现加权Möller算法稳定性在动力学层面上的分析, 探讨加权参数变化对算法稳定性的影响.基于常微分方程方法对所提出规则下的加权Möller算法进行稳定性证明, 并分析其中关键函数的性质.最后, MATLAB仿真验证了所提出规则的性能和算法性质.Abstract: A generalized weighted rule for weighted Möller algorithm is introduced to explore the modified minor component analysis by parallel extraction in theory and application. The proposed rule helps to analyze the stability in the dynamic of the algorithm in aspects of different properties, through altering the generalized weighted parameter, which is the only alterable parameter adopted in the weighted Möller algorithm. The stability analysis of the weighted Möller algorithm modified by the proposed generalized weighted rule is evaluated based on ordinary differential equation. And the analysis of the key functions is given. Finally, the properties of the modified algorithms and the ability of the proposed rule are verified by simulations in MATLAB.
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Key words:
- Multiple minor components /
- generalized weighted rule /
- parallel extraction /
- Möller algorithm
1) 本文责任编委 谭营 -
图 2 $\delta w$的变化, $p=1$处用深色标示
Fig. 2 Change of $\delta w$ where $p=1$ is marked in deep color
图 3 方向余弦曲线(上为$p=0.6$, 下为$p=1.5$)
Fig. 3 Curves of the direction cosine ($p=0.6$ is on the top and $p=1.5$ is at the bottom)
图 4 估计模值曲线(上为$p=0.6$, 下为$p=1.5$)
Fig. 4 Curves of the estimated norm ($p=0.6$ is on the top and $p=1.5$ is at the bottom)
图 5 特征值变化(上为$p=0.6$, 下为$p=1.5$)
Fig. 5 Curves of the eigenvalues ($p=0.6$ is on the top and $p=1.5$ is at the bottom)
图 6 正交性变化(上为$p=0.6$, 下为$p=1.5$)
Fig. 6 Curves of the orthogonality ($p=0.6$ is on the top and $p=1.5$ is at the bottom)
图 7 $\delta w$值变化(上为$p=0.6$, 下为$p=1.5$)
Fig. 7 Curves of $\delta w$ ($p=0.6$ is on the top and $p=1.5$ is at the bottom)
表 1 不同的$p$对应的重构误差值
Table 1 Reconstruction error rates for different $p$
$p$ 0.6 0.8 1.0 1.2 1.5 重构误差值(%) 16.383 20.126 22.878 29.369 31.047 
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