Robust Independent Component Analysis by Iterative Maximization of the Kurtosis Contrast With Algebraic Optimal Step Size
Robust Independent Component Analysis by Iterative Maximization of the Kurtosis Contrast With Algebraic Optimal Step Size
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DOI：
10.1109/tnn.2009.2035920
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发表时间：
2010-02-01
影响因子：
--
通讯作者：
Comon, Pierre
中科院分区：
文献类型：
--
作者：
Zarzoso, Vicente;Comon, Pierre
独立分量分析(ICA)的目的是将观测到的随机向量分解为统计独立变量。基于通货紧缩的实现，如流行的一单元FastICA算法及其变体，一个接一个地提取独立分量。本文提出了一种新的通货紧缩独立分量分析方法--RobustICA。这种简单的技术包括对峰度对比度函数进行精确线搜索优化。在四次多项式的根中找到导致沿搜索方向的对比度的全局最大值的步长。这种多项式求根可以在每次迭代中以代数方式执行，从而以低成本执行。在其他实际好处中，RobustICA可以避免预白化，并可以处理可能是非圆形源的实值和复值混合。没有预白化可以提高渐近性能。该算法对局部极值具有较强的鲁棒性，并且在达到给定源提取质量所需的计算代价方面表现出很高的收敛速度，特别是对于较短的数据记录。通过对合成数据的对比数值分析，证明了这些特征。RobustICA在处理包含非圆形复杂强超高斯源的真实世界数据方面的能力被心房颤动(AF)心电(ECGs)中的心房活动(AA)提取的生物医学问题所证明，它的性能优于基于ICA的替代技术。
Independent component analysis (ICA) aims at decomposing an observed random vector into statistically independent variables. Deflation-based implementations, such as the popular one-unit FastICA algorithm and its variants, extract the independent components one after another. A novel method for deflationary ICA, referred to as RobustICA, is put forward in this paper. This simple technique consists of performing exact line search optimization of the kurtosis contrast function. The step size leading to the global maximum of the contrast along the search direction is found among the roots of a fourth-degree polynomial. This polynomial rooting can be performed algebraically, and thus at low cost, at each iteration. Among other practical benefits, RobustICA can avoid prewhitening and deals with real-and complex-valued mixtures of possibly noncircular sources alike. The absence of prewhitening improves asymptotic performance. The algorithm is robust to local extrema and shows a very high convergence speed in terms of the computational cost required to reach a given source extraction quality, particularly for short data records. These features are demonstrated by a comparative numerical analysis on synthetic data. RobustICA's capabilities in processing real-world data involving noncircular complex strongly super-Gaussian sources are illustrated by the biomedical problem of atrial activity (AA) extraction in atrial fibrillation (AF) electrocardiograms (ECGs), where it outperforms an alternative ICA-based technique.