ROSA-a fast extension of partial least squares regression for multiblock data analysis

We present the response-oriented sequential alternation (ROSA) method for multiblock data analysis. ROSA is a novel and transparent multiblock extension of the partial least squares regression (PLSR). According to a "winner takes all" approach, each component of the model is calculated from the block of predictors that most reduces the current residual error. The suggested algorithm is computationally fast compared with other multiblock methods because orthogonal scores and loading weights are calculated without deflation of the predictor blocks. Therefore, it can work effectively even with a large number of blocks included. The ROSA method is invariant to block scaling and ordering. The ROSA model has the same attributes (vectors of scores, loadings, and loading weights) as PLSR and is identical to PLSR modeling for the case with only one block of predictors.