用于磁共振波谱（MRS）和脑电图（EEG）信号独立成分分析的累积量矩阵联合对角化
On joint diagonalization of cumulant matrices for independent component analysis of MRS and EEG signals.
作者信息
Albera Laurent, Kachenoura Amar, Wendling Fabrice, Senhadji Lotfi, Merlet Isabelle
机构信息
INSERM U642, Rennes F-35000, France, and the Université de Rennes 1, LTSI, F-35000, France.
出版信息
Annu Int Conf IEEE Eng Med Biol Soc. 2010;2010:1902-5. doi: 10.1109/IEMBS.2010.5627334.
An extension of the original implementation of JADE, named eJADE((1)) hereafter, was proposed in 2001 to perform independent component analysis for any combination of statistical orders greater than or equal to three. More precisely, eJADE((1)) relies on the joint diagonalization of a set of several cumulant matrices corresponding to different matrix slices of one or several higher order cumulant tensors. An efficient way, without lose of statistical information, of reducing the number of third and fourth order cumulant matrices to be jointly diagonalized is proposed in this paper. The resulting approach, named eJADE(3,4)((2)), can be interpreted as an improvement of the eJADE(3,4)((1)) method. A performance comparison with classical methods is conducted in the context of MRS and EEG signals showing the good behavior of our technique.
2001年提出了JADE原始实现的一个扩展版本，此后称为eJADE((1))，用于对任何大于或等于三阶的统计阶数组合进行独立成分分析。更确切地说，eJADE((1))依赖于一组对应于一个或几个高阶累积量张量的不同矩阵切片的累积量矩阵的联合对角化。本文提出了一种在不损失统计信息的情况下，减少需要联合对角化的三阶和四阶累积量矩阵数量的有效方法。由此产生的方法称为eJADE(3,4)((2))，可以解释为对eJADE(3,4)((1))方法的改进。在磁共振波谱（MRS）和脑电图（EEG）信号的背景下，与经典方法进行了性能比较，结果表明我们的技术表现良好。
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