Functions to perform sequential mutiblock PLS (SMB-PLS) modeling.

Original codes developed in Matlab by Lauzon-Gauthier et al. and adapted to Python in this package.
Package includes following functions:
-data normalization: normalisation_data, normalisation_data_val.
-block data normalization: normalisation_blocs_cal, normalisation_blocs_val.
-SMB-PLS: smbplsnipals, smbpls_cal, smbpls_exploit.
-Random-subset (RS) cross-validation: rs_cv.
-Predictive performances: VIP, BIP, CalculR, SPELimit, SPECalculation.

Lauzon-Gauthier, J., Manolescu, P., & Duchesne, C. (2018). The Sequential Multi-block PLS algorithm (SMB-PLS): Comparison of performance and interpretability. Chemometrics and Intelligent Laboratory Systems, 180(May), 72–83. https://doi.org/10.1016/j.chemolab.2018.07.005

Call function

model = smbpls_cal(xc,yc,bl,lv)

predictions = smbpls_exploit(xv,yv,bl,model)

Input arguments

1. xc (n1,k1): X-blocks concatenated for SMB-PLS calibration.
2. yc (n1,ky): Y-block - reference values for calibration dataset.
3. xv (n2,k1): X-blocks concatenated for SMB-PLS calibration.
4. yv (n2,1): Y-block - reference values for validation dataset.
5. bl (list of lists): List of variable indices for each X block. Each sublist corresponds to a block and contains the indices of its variables in the global X-matrix.
6. lv (n_blocks,1): Number of latent variables per block.

Outputs

1. model (dict): Contains the SMB-PLS model parameters, including scores, loadings and predictions.
   Key entries include:
   -model['ypred']: Predicted response values from SMB-PLS.
   -model['Wsuper']: Super weights matrix (n_blocks, total_latent_variables).
   -model['Wblock']: Block weights matrix (matrix per block).
2. predictions (dict): Contains SMB-PLS prediction results obtained by applying the model to a validation dataset.
   -predictions['ypred']: Predicted response on the validation set.

Examples

One full example, along with dataset is provided in folder 'tests' of 'Download Files'.

• Example 1: Grinding flotation simulator dataset (provided by Paris et al.)

Research using SMB-PLS:

Paris, A., Duchesne, C., & Poulin, É. (2021). Establishing multivariate specification regions for incoming raw materials using projection to latent structure models: comparison between direct mapping and model inversion. Frontiers in Analytical Science, 1(November), 1–15. https://doi.org/10.3389/frans.2021.729732.

Paris, A., Duchesne, C., & Poulin, É. (2024). Adjusting plant operating conditions to widen multivariate specification regions for incoming raw materials – An optimization framework. Chemometrics and Intelligent Laboratory Systems, 244(September 2023). https://doi.org/10.1016/j.chemolab.2023.104991.

Paris, A., Duchesne, C., & Poulin, É. (2024). Improving profitability of continuous processes facing raw material variability through data-driven SMB-PLS model-based adaptive control. Computers and Chemical Engineering, 184(October 2023). https://doi.org/10.1016/j.compchemeng.2024.108615.

Compatibility

smb_pls tested on Python 3.11 using the following modules:

• numpy 1.24.4
• matplotlib 3.10.1
• SciPy 1.15.2