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首页> 外文期刊>IEEE Transactions on Neural Networks >Local Convergence Analysis of FastICA and Related Algorithms
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Local Convergence Analysis of FastICA and Related Algorithms

机译：FastICA的局部收敛性分析及相关算法

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摘要

The FastICA algorithm is one of the most prominent methods to solve the problem of linear independent component analysis (ICA). Although there have been several attempts to prove local convergence properties of FastICA, rigorous analysis is still missing in the community. The major difficulty of analysis is because of the well-known sign-flipping phenomenon of FastICA, which causes the discontinuity of the corresponding FastICA map on the unit sphere. In this paper, by using the concept of principal fiber bundles, FastICA is proven to be locally quadratically convergent to a correct separation. Higher order local convergence properties of FastICA are also investigated in the framework of a scalar shift strategy. Moreover, as a parallelized version of FastICA, the so-called QR FastICA algorithm, which employs the QR decomposition (Gram–Schmidt orthonormalization process) instead of the polar decomposition, is shown to share similar local convergence properties with the original FastICA.
机译：FastICA算法是解决线性独立分量分析（ICA）问题的最著名方法之一。尽管已经进行了几次尝试来证明FastICA的局部收敛性，但是社区中仍然缺少严格的分析。分析的主要困难是由于众所周知的FastICA符号翻转现象，导致相应的FastICA映射在单位球面上的不连续性。在本文中，通过使用主光纤束的概念，FastICA被证明是局部二次收敛到正确的分离。 FastICA的高阶局部收敛性也在标量移位策略的框架内进行了研究。此外，作为FastICA的并行化版本，使用QR分解（Gram–Schmidt正交归一化过程）而非极性分解的所谓QR FastICA算法被证明与原始FastICA具有相似的局部收敛性。

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