Segmented principal component transform–principal component analysis

A new approach to perform Principal Component Analysis (PCA) on very wide matrices is proposed in this work. The procedure is based on an extension of the Principal Component Transform (PCT) concept—the PCT being applied to non-superimposed segments of the data matrix. It is shown that this method uses less memory than the classical global PCA since the decomposition is done on much smaller matrices, which has an important impact on the memory requirements. It is also shown that the Segmented PCT-PCA (SegPCT-PCA) yields the same results as the decomposition performed by a global PCA. This approach will allow the study of very wide data sets (e.g. 2D-NMR), which were difficult to do using the global PCA approach. The implementation of SegPCT-PCA is straightforward. An advantage of the method is that it is not necessary to read the complete matrix into the main memory, which could be an advantage for parallel calculations and for cross-validation purposes.