Independent Components Analysis with the JADE algorithm

• Independent Components Analysis compared to Principal Components Analysis.
• Extraction of interpretable signals from complex data sets.
• Application of Independent Components Analysis to multiway data arrays.

Independent Components Analysis (ICA) is a relatively recent method, with an increasing number of applications in chemometrics. Of the many algorithms available to compute ICA parameters, the Joint Approximate Diagonalization of Eigenmatrices (JADE) algorithm is presented here in detail. Three examples are used to illustrate its performance, and highlight the differences between ICA results and those of other methods, such as Principal Components Analysis. A comparison with Parallel Factor Analysis (PARAFAC) is also presented in the case of a three-way data set to show that ICA applied on an unfolded high-order array can give results comparable with those of PARAFAC.