Swiss knife covariates selection: A unified algorithm for covariates selection in single block, multiblock, multiway, multiway multiblock cases including multiple responses

Abstract

A novel unified covariates selection algorithm called Swiss knife covariates selection (SKCovSel) is presented. It is suitable for selecting covariates in a wide range of data scenarios such as a single two‐way data block, two‐way multiblock, multiway, multiway multiblock, selection of covariates along different modes for multiway data blocks and for selecting covariates for all mentioned cases in multiple response scenarios. In the multiblock case, the method can be scale and data block order‐independent depending on the preference of the user. For multiway scenarios, the method can be multiway mode order independent, depending on the preference of the user. The proposed SKCovSel algorithm generalises the recent speed improvements from faster CovSel to all mentioned data block cases. It also reformulates the multiway case to do proper deflation and rank one slab selections. Particularly, for modelling of multiblock data sets, the SKCovSel follows the “winner takes all” strategy of the stepwise response‐oriented sequential alternation modelling. In the case of multiway data, the SKCovSel strategy considers multiway loading weights after decomposition of a high‐dimensional squared covariance matrix to select features across different modes. The algorithmic steps of the methods are presented, and cases of modelling different data types such as single block, multiblock, multiway multiblock, modes selection for multiway data and multiple responses modelling are shown. The method incorporates all popular covariates selection algorithms existing in the chemometric literature.

Iterative re‐weighted multilinear partial least squares modelling for robust predictive modelling

“…Furthermore, the residuals from multiple responses can be jointly handled as a product as done in earlier works 18,26 . The same algorithm can also be adapted to do higher order robust feature selection 18 for multilinear data with methods such as N‐way covariates selection 31 . The feature selection step will involve binarising the robust loading weight vector using a criterion such as maximum covariance.…”

Distributed statistical process monitoring based on block‐wise residual generator

“…This kind of block division was suggested by Zhu et al 37 who argued that the condenser and compressor both involve just one measured variable, and they could more appropriately be allocated to the nearby reactor and separator blocks, respectively. If the interaction between the production units is additionally considered, an overlapped block division (marked as MB3) proposed by Wan et al 21 could also be a rational choice, which is detailed in Table 3.…”

“…[18][19][20] With respect to the increasing scale of modern chemical processes, distributed process monitoring has been a growing branch for the last decade. [21][22][23][24][25][26] Because large-scale chemical processes generally consist of multiple units as well as plenty of measured variables, the interpretability of data-driven models could be enhanced if the normal variation in the given dataset is modeled from multi-block or distributed aspect. 21 Mishra et al 22 provided a comprehensive review for recent trends in multi-block data analytical methods.…”

“…[21][22][23][24][25][26] Because large-scale chemical processes generally consist of multiple units as well as plenty of measured variables, the interpretability of data-driven models could be enhanced if the normal variation in the given dataset is modeled from multi-block or distributed aspect. 21 Mishra et al 22 provided a comprehensive review for recent trends in multi-block data analytical methods. An examination of existing literature with a topic of distributed process monitoring shows that dividing the whole set of measured variables into multiple subsets, termed as block division (or variable division), is always the initial step, which is then followed by diverse multi-block modeling approaches.…”