Independent component analysis (ICA) is a ubiquitous method for decomposing complex signal mixtures into a small set of statistically independent source signals. However, in cases in which the signal mixture consists of both nongaussian and Gaussian sources, the Gaussian sources will not be recoverable by ICA and will pollute estimates of the nongaussian sources. Therefore, it is desirable to have methods for mixed ICA/PCA which can separate mixtures of Gaussian and nongaussian sources. For mixtures of purely Gaussian sources, principal component analysis (PCA) can provide a basis for the Gaussian subspace. We introduce a new method for mixed ICA/PCA which we call >Mixed >ICA/>PCA via >Reproducibility >Stability (MIPReSt). Our method uses a repeated estimations technique to rank sources by reproducibility, combined with decomposition of multiple subsamplings of the original data matrix. These multiple decompositions allow us to assess component stability as the size of the data matrix changes, which can be used to determinine the dimension of the nongaussian subspace in a mixture. We demonstrate the utility of MIPReSt for signal mixtures consisting of simulated sources and real-word (speech) sources, as well as mixture of unknown composition.
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机译：独立分量分析（ICA）是一种将复杂信号混合物分解为一小组统计独立的源信号的普遍方法。但是，在信号混合同时包含非高斯和高斯源的情况下，ICA将无法恢复高斯源，并且会污染非高斯源的估计值。因此，期望具有可以分离高斯和非高斯源的混合物的ICA / PCA混合方法。对于纯高斯源的混合，主成分分析（PCA）可以为高斯子空间提供基础。我们介绍了一种用于混合ICA / PCA的新方法，称为“ > M 固定的> I CA / > P CA通过> Re 生产能力> St 能力（MIPReSt）。我们的方法使用重复估计技术，通过可再现性对源进行排序，并结合原始数据矩阵的多个子采样的分解。这些多重分解使我们能够随着数据矩阵大小的变化来评估组件的稳定性，这可以用来确定混合物中非高斯子空间的大小。我们演示了MIPReSt在混合信号（包括模拟源和实词（语音）源）以及未知成分的混合信号中的实用性。
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