基于互信息的最小相关分量分析
Least Dependent Component Analysis Based on Mutual Information
摘要：
我们建议使用互信息（MI）的精确估计来找到线性混合信号中最不相关的分量。一方面，这似乎导致更好的盲源分离比任何其他目前可用的算法。另一方面，与“独立”分量分析（ICA）的其他实现（其中一些基于MI的粗略近似）相比，它具有以下优点：MI的数值可以用于：（i）估计输出分量之间的残差依赖性;（ii）通过将成对MI与重新混合分量的MI进行比较来估计输出的可靠性;（iii）根据剩余的相互依赖性对输出进行聚类。对于MI估计，我们使用最近提出的基于k-近邻的算法。对于时间序列，我们将其与延迟嵌入相结合，以考虑非平凡的时间相关性。经过几次人工数据的测试，我们将得到的MILCA（基于互信息的最小依赖分量分析）算法应用于真实世界的数据集，孕妇的心电图。MILCA算法的软件实现可在http://www.fz-juelich.de/nic/cs/software上免费获得
英文摘要：
We propose to use precise estimators of mutual information (MI) to find least dependent components in a linearly mixed signal. On the one hand this seems to lead to better blind source separation than with any other presently available algorithm. On the other hand it has the advantage, compared to other implementations of `independent' component analysis (ICA) some of which are based on crude approximations for MI, that the numerical values of the MI can be used for: (i) estimating residual dependencies between the output components; (ii) estimating the reliability of the output, by comparing the pairwise MIs with those of re-mixed components; (iii) clustering the output according to the residual interdependencies. For the MI estimator we use a recently proposed k-nearest neighbor based algorithm. For time sequences we combine this with delay embedding, in order to take into account non-trivial time correlations. After several tests with artificial data, we apply the resulting MILCA (Mutual Information based Least dependent Component Analysis) algorithm to a real-world dataset, the ECG of a pregnant woman. The software implementation of the MILCA algorithm is freely available at http://www.fz-juelich.de/nic/cs/software
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