Comparison of projection pursuit to independent component analysis

Projection pursuit (PP) and independent component analysis (ICA) are two approaches to the blind source separation problem. In principle, ICA looks for maximum independence of resolved source vectors, while PP optimizes measures of non-Gaussianity. Similarities and differences between ICA and PP are considered in many sources, but the comparisons are largely vague. A number of reports state that PP is a sequential extraction technique, while ICA employs a simultaneous method [1]; however multivariate PP is simultaneous [2] and FastICA [3] is a sequential approach. One practical difference between ICA and PP is that the non-Gaussianity measure is enforced on the scores for PP and on the loadings for ICA. On the other hand, uncorrelated and non-Gaussian behavior are the basis criteria for resolved profiles from many PP and ICA algorithms. Thus, it is not hard to see why some believe PP and ICA are the same. In case of truly independent signals, such as those from acoustic sources, PP can separate real source vectors comparable to ICA. However, utilizing simulated and experimental data, it was observed that neither of the two methods could resolve spectrochemical data into the real source vectors. ICA [4], like PP [2] could be applied for clustering of the NIR spectra from ink samples and unsupervised classification of archeological data. Preprocessing is very effective on results from PP and ICA. Applying the same criterion as an objective function in PP and ICA, they can be regarded as essentially equivalent. When the real source vectors have maximum possible leptokurtic solutions with maximum kurtosis values (the solution that is most separated from Gaussianity) both PP and ICA can successfully be applied for the resolution of actual source vectors. It is not usually the case for spectrochemical data in which the real source vectors are not the most independent and non-Gaussian among the possible solutions. Although using different criteria, the results from PP and ICA are similar in their estimation of actual source vectors from some types of mixture signals but not from spectrochemical signals. The clustering ability of PP and ICA are comparable.