This work presents sparse invariant coordinate analysis, SICS, a new method for sparse and robust independent component analysis. SICS is based on classical invariant coordinate analysis, which is presented in such a form that a LASSO-type penalty can be applied to promote sparsity. Robustness is achieved by using robust scatter matrices. In the first part of the paper, the background and building blocks: scatter matrices, measures of robustness, ICS and independent component analysis, are carefully introduced. Then the proposed new method and its algorithm are derived and presented. This part also includes a consistency result for a general case of sparse ICS-like methods. The performance of SICS in identifying sparse independent component loadings is investigated with simulations. The method is also illustrated with example in constructing sparse causal graphs.

翻译：本研究提出了一种新的稀疏稳健独立成分分析方法——稀疏不变坐标分析（SICS）。该方法基于经典的不变坐标分析，并通过引入LASSO型惩罚项以促进稀疏性。通过采用稳健散点矩阵实现方法的稳健性。论文第一部分系统介绍了相关背景与基础构件：散点矩阵、稳健性度量、不变坐标分析及独立成分分析。随后推导并阐述了所提出的新方法及其算法，该部分还包含针对一类稀疏不变坐标分析方法的通用一致性结果。通过模拟实验研究了SICS在识别稀疏独立成分载荷方面的性能，并以构建稀疏因果图为例展示了该方法的应用。