提出鲁棒独立成分分析新方法，有效处理数据中的异常值。
Independent Component Analysis by Robust Distance Correlation
- 用改进的距离相关性度量依赖关系，结合碗变换增强抗异常值能力。
- 在模拟实验中性能优于现有方法，对异常值不敏感且收敛速度快。
- 适合信号分离、数据清洗等存在噪声或异常的数据分析场景。
独立成分分析（ICA）能将多变量信号分解为完全独立的源信号，而不仅是不相关的。然而，多数ICA方法对异常值不鲁棒。本文提出一种名为RICA的新方法，通过最小化多变量随机变量间的鲁棒依赖度量来估计成分。该度量基于距离相关性（dCor），并引入新的碗变换：其为有界、一一对应、连续映射，可将远端异常值压缩至原点附近，同时保持dCor为零即意味着独立的关键性质。RICA按顺序估计独立源，每次寻找与剩余部分距离相关性最小的分量。理论证明其强一致性及标准参数收敛速率。模拟研究表明，RICA在多种情形下普遍优于现有方法。实际应用包括著名的鸡尾酒会问题等三个案例。
原文摘要 · Abstract (English)
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.
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