In the presentation of a data set made up of an aggregate of several clusters, we may say that, for the clusters to be individually visible, the separation between them has to be larger than the internal scatter of the clusters. If it happens that there are only a few clusters in the data set, then the leading principal axes found by PCA are to pick projections of the clusters with good separation, thereby providing an effective basis for feature extraction.
Another application of the principal-components analyzer as a preprocessor is in the supervised training of a multilayer perceptron using the back-propagation algorithm. The aim in this application is to speed up the convergence of the learning process by decorrelating the input data. Discuss how this aim is realized.