Modelling procedures for directed network of data blocks

Here are presented procedures for modelling data in a network. The methods are extensions of PCA or PLS regression to a forward network of data blocks. It is assumed that the data blocks are organised in a network such that one data block leads to one or more other data blocks. The procedures are stepwise ones. At each step a passage through the network is carried out. From the input weight vectors of the input or starting blocks, the score and loading vectors of all data blocks are computed. It is investigated if some score/loading vectors are not significant. If some are, they are deleted and revised estimation of the input weights are carried out. When one step is finished, all data matrices are adjusted for score and loading vectors found. A new passage through the network is carried out on the reduced matrices. If no significant loading/score vectors are found for a given set of input weights, the modelling stops. In case of one data block, the algorithm reduces to PCA. In case of two data blocks it reduces to PLS regression. Most methods used in PCA or PLS regression can be applied to this procedure, e.g., cross-validation and re-sampling procedures. It is pointed out, how these methods can be used to extend other regression methods than PCA and PLS regression to a network regression. (C) 2008 Elsevier B.V. All rights reserved.