Cross validation and uncertainty estimates in independent component analysis

A data analysis tool, known as independent component analysis (ICA), is the main focus of this paper. The theory of ICA is briefly reviewed, and the underlying statistical assumptions and a practical algorithm are described. This paper introduces cross validation/jack-knifing and significance tests to ICA. Jack-knifing is applied to estimate uncertainties for the ICA loadings, which also serve as a basis for significance tests. These tests are shown to improve ICA performance, indicating how many components are mixed in the observed data, and also which parts of the extracted sources that contain significant information. We address the issue of stability for the ICA model through uncertainty plots. The ICA performance is compared to principal component analysis (PCA) for two selected applications, a simulated experiment and a real world application.