The fastICA method is a popular dimension reduction technique used to reveal patterns in data. Here we show both theoretically and in practice that the approximations used in fastICA can result in patterns not being successfully recognised. We demonstrate this problem using a two-dimensional example where a clear structure is immediately visible to the naked eye, but where the projection chosen by fastICA fails to reveal this structure. This implies that care is needed when applying fastICA. We discuss how the problem arises and how it is intrinsically connected to the approximations that form the basis of the computational efficiency of fastICA.

中文翻译：

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FastICA算法中熵的估计

fastICA 方法是一种流行的降维技术，用于揭示数据中的模式。在这里，我们在理论上和实践中都表明，fastICA 中使用的近似值会导致无法成功识别模式。我们使用一个二维示例来演示这个问题，其中肉眼可以立即看到清晰的结构，但是 fastICA 选择的投影无法揭示这种结构。这意味着在应用 fastICA 时需要小心。我们讨论问题是如何产生的，以及它如何与构成 fastICA 计算效率基础的近似值有内在联系。