Independent component analysis (ICA) is a powerful tool for decomposing a multivariate signal or distribution into fully independent sources, not just uncorrelated ones. Unfortunately, most approaches to ICA are not robust against outliers. Here we propose a robust ICA method called RICA, which estimates the components by minimizing a robust measure of dependence between multivariate random variables. The dependence measure used is the distance correlation (dCor). In order to make it more robust we first apply a new transformation called the bowl transform, which is bounded, one-to-one, continuous, and maps far outliers to points close to the origin. This preserves the crucial property that a zero dCor implies independence. RICA estimates the independent sources sequentially, by looking for the component that has the smallest dCor with the remainder. RICA is strongly consistent and has the usual parametric rate of convergence. Its robustness is investigated by a simulation study, in which it generally outperforms its competitors. The method is illustrated on three applications, including the well-known cocktail party problem.

翻译：独立成分分析（ICA）是一种强大的工具，能够将多元信号或分布分解为完全独立的源信号，而不仅仅是互不相关的成分。然而，大多数ICA方法对异常值不具备鲁棒性。本文提出了一种名为RICA的鲁棒ICA方法，该方法通过最小化多元随机变量之间依赖性的鲁棒度量来估计独立成分。所使用的依赖性度量是距离相关（dCor）。为了增强其鲁棒性，我们首先应用一种称为碗变换的新变换，该变换具有有界性、一一对应性、连续性，并将远处的异常值映射到接近原点的位置。这保留了距离相关为零意味着独立性的关键性质。RICA通过顺序寻找与剩余部分具有最小距离相关的成分来估计独立源信号。RICA具有强一致性，并具有通常的参数收敛速率。通过模拟研究验证了其鲁棒性，结果表明RICA通常优于其他方法。该方法在三个应用实例中得到了演示，包括著名的鸡尾酒会问题。