Hyvärinen A
Helsinki University of Technology, Laboratory of Computer and Information Science, FIN-02015 HUT, Finland.
IEEE Trans Neural Netw. 1999;10(3):626-34. doi: 10.1109/72.761722.
Independent component analysis (ICA) is a statistical method for transforming an observed multidimensional random vector into components that are statistically as independent from each other as possible. In this paper, we use a combination of two different approaches for linear ICA: Comon's information-theoretic approach and the projection pursuit approach. Using maximum entropy approximations of differential entropy, we introduce a family of new contrast (objective) functions for ICA. These contrast functions enable both the estimation of the whole decomposition by minimizing mutual information, and estimation of individual independent components as projection pursuit directions. The statistical properties of the estimators based on such contrast functions are analyzed under the assumption of the linear mixture model, and it is shown how to choose contrast functions that are robust and/or of minimum variance. Finally, we introduce simple fixed-point algorithms for practical optimization of the contrast functions. These algorithms optimize the contrast functions very fast and reliably.
独立成分分析（ICA）是一种统计方法，用于将观测到的多维随机向量转换为彼此在统计上尽可能独立的成分。在本文中，我们使用两种不同的线性ICA方法的组合：科蒙的信息论方法和投影寻踪方法。利用微分熵的最大熵近似，我们为ICA引入了一族新的对比（目标）函数。这些对比函数既能通过最小化互信息来估计整个分解，又能将各个独立成分估计为投影寻踪方向。在线性混合模型的假设下，分析了基于此类对比函数的估计器的统计特性，并展示了如何选择稳健和/或方差最小的对比函数。最后，我们引入了用于对比函数实际优化的简单定点算法。这些算法能非常快速且可靠地优化对比函数。
