Cyclic Subspace Regression

By use of cyclic subspaces, explicit connections between principal component regression (PCR) and partial least squares (PLS) are established that shed light onto why one method works better than the other. These connections clearly identify how both methods make use of calibration data in prediction. Moreover, developments leading to these connections show that they are particular manifestations of a more general easily described and implemented regression/prediction process referred to as cyclic subspace regression (CSR). This process not only contains PCR, PLS, and LS (least squares) as special cases but, also a finite number of other related intermediate or transitional regression techniques. Moreover, CSR shows that PCR, PLS, LS, and the related intermediates can be implemented by the same general procedure and that they differ only in the amount of information used from calibration data matrices. In addition to setting out the CSR procedure, the paper also supplies a robust numerical algorithm for its implementation which is used to show how procedures contained within CSR perform on a chemical data set.