摘要:通过引入一个用于评价多维独立成分分析(MICA)算法性能的指标，进行数值仿真来研究其分离性。将多维Amari分离误差作为度量多维独立成分分析算法性能的一个重要指标，在比较分析研究vkMICA、cfMICA、MSOBI、SJADE等四个算法的分离性能的基础上，使用随机分布生成的字母信号进行仿真与测试，直观地显示了MICA模型的分离效果和不确定性。研究结果显示，MICA是一种非常有效的进行多维源信号分析的方法。
关键词:多维独立成分分析；多维Amari； 数值仿真；信号测试
中图分类号: TP301.6；O242.1 文献标志码:A
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Numerical simulation and analysis based on �multidimensional independent component analysis
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XIE Yong.hong��1�*�, ZHANG Guo.wei�2
�(1.Department of Computer Science, Harbin Finance University, Harbin Heilongjiang 150030, China
;�
2.School of Electronics and Information Engineering, Xi�an Jiaotong University, Xi�an Shaanxi 710049, China
Abstract:
By introducing a indicator to evaluate performance of Multidimensional Independent Component Analysis (MICA) algorithm, the separation was studied by numerical simulation. Using multidimensional Amari separation error as an important indicator of a measurement of multidimensional independent component analysis algorithm performance. In the comparative analysis of four algorithm named vkMICA, cfMICA, MSOBI, SJADE in the separation performance, a random distribution of letters signal was used for simulation and testing, and get a visual representation of MICA model of separation and uncertainty. The results show that MICA is a very effective method for multidimensional source signal analysis.
By introducing an indicator to evaluate performance of Multidimensional Independent Component Analysis (MICA) algorithm, the separation was studied by numerical simulation. The multidimensional Amari separation error was used as an important indicator of the measurement of MICA algorithm performance. In the comparative separation performance analysis of four algorithms named vkMICA, cfMICA, MSOBI, SJADE, a random distribution of letters signal was used for simulation and testing, and a visual representation of MICA model of separation and uncertainty was got. The results show that MICA is a very effective method for multidimensional source signal analysis.�Key words:
Multidimensional Independent Component Analysis (MICA); multidimensional Amari; numerical simulation; signal testing
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0 引言�
法国学者Cardoso��［1］�于1998年首先给出了标准的多维独立成分分析(Multidimensional Independent Component Analysis, MICA)定义，提出了加法模型并通过几何参数化方法对MICA的算法进行分解。MICA算法估计的系统框架如图1所示。�
在图1中，�A是混合矩阵，V是白化矩阵，U是局部的正交分离矩阵，B是利用算法最终确定的全局解混矩阵，它实际上是对A��－1�的估计，而得到的y�是对源的估计。所以，MICA估计算法的中心任务就是确定分离矩阵�B，使得能够对源S【图上是小写？】或混合矩阵A�实现有效地估计。对于MICA估计算法，可分为批处理(离线)和在线算法，把批处理算法结合独立成分分析（Independent Component Analysis，ICA）算法，并将其推广到多维的情况，从而讨论四种MICA算法的分离性能，即基于向量峭度的不动点算法��［2］�(vector kurtosis based MICA, vkMICA)，基于第二特征函数Hessian矩阵联合块对角化的算法��［3］�(characteristic function based MICA, cfMICA)， 基于特征矩阵联合块对角化的算法��［4］�(Subspace JADE, SJADE)和基于时延协方差矩阵联合块对角化的算法��［5］�(Multidimensional Second Order Blind Identification, MSOBI)。通过引入一个用于评价MICA算法性能的指标，进行数值仿真来研究其分离性。�
2.2 处理点数�K�的选取对算法的影响�
以cfMICA算法为例，使用式(7)所示的混合矩阵得到观测信号�X(t)=As(t)，取处理点数K分别为K=10,20,…,100，对每个K分别运行50次，得到混合矩阵的估计A�U，求取每个K�对应的平均多维Amari分离误差�E��(2)�(A��U����-1���A)，得到的结果如图5所示。�
由图5可知，对于不同的处理点数K，算法的分离误差E��(2)�(A��U����-1���A)约为0.05�9，且波动范围不大，这说明在处理点选取为［-0.025,0.025］的均匀分布时，处理点的个数对于算法的性能并无明显的影响，算法是比较稳健的。但当K=60�时，分离误差是最小的，故在比较各算法的性能时，将选取此值。�
2.3 时延个数�L�的选取对算法的影响�
以MSOBI算法为例，仍然使用式(7)所示的混合矩阵得到观测信号�X(t)=As(t)，取时延个数分别为L=10,20,…,100，对每个L分别运行50次，得到混合矩阵的估计A�U，求取每个L�对应的平均多维Amari分离误差�E��(2)�(A��U����-1���A)，�得到的结果如图6所示。�
4 结语�
本文检测了MICA的四个算法的性能指标，主要分析了处理点的个数的选取、不同时延个数的选取对算法的影响；在无噪声和有噪声条件下，基于联合块对角化(JBD)的CFMICA、SJADE、MSOBI三个算法都表现了一定的抗噪声性能。但当高能量的噪声下，需要在算法处理前加上降噪处理环节。仿真与测试分析表明，四个算法均能够在一定程度上完成对源信号的分离，在此基础上，再进行联合块对角化的协方差矩阵相应增加，从而更好地反映了信号空间的“平均特征”，得到更好的分离效果。MICA的算法可以非常有效地进行多维源信号分析，也是后期研究和实际应用的内容。 �
图片
图12 以SJADE算法为例分析得到的对3个字母信号的估计�参考文献:�
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