Is there any way to fit a single PLS model to several training datasets?
Let X1, X2 and X3 be the predictive variables matrices and Y1, Y2 and Y3 the output variables of 3 different datasets. I would like to find a single PLS model that is trained based on all 3 datasets at the same time. I would not prefer to define X=[X1;X2;X3] and Y=[Y1;Y2;Y3] and perform PLS on X and Y, since the means of each dataset is slightly different and autoscaling would be based on the dominant dataset. Also the X and Y would have discontinuation at the points where Xi and Yi s are merged.
I am not sure if the multi-block PLS (MBPLS) could solve my problem since in the MBPLS algorithm the sub-levels (X1,X2 and X3 in my case) are used both in training and testing steps. In other words, once you develop the MBPLS model, you still need the sub-levels to test your model.
What I am looking for is to find a PLS model fitted to several data-sets simultaneously, but still test the model with single data-sets separately:
pls_model= train with X1, X2, X3 and Y1, Y2, Y3 at the same time
predict_Y1= test the pls_model on X1 (and Y1)
predict_Y2= test the pls_model on X2 (and Y2)
predict_Y3= test the pls_model on X3 (and Y3)
Still not sure about your point. If you develop the PLS using multiple y-vectors then the model will search for some parameters for the relationship between e.g. X1-Y2 and X1-Y3 etc. I already know, Y1 has nothing with X2 or X3 (same for Y2 and Y3).
Also if I define X=[X1 X2 X3] and Y=[Y1 Y2 Y3] and then develop a PLS model with X and Y, it will give the priority to the variable(s) (in X) and output(s) (in Y) that has the most variation comparing to others. The direction of the first latent variable will describe the direction of the most variant output. The less important outputs (according to variation) will be modeled with higher latent variables. in In my case all outputs are considered to be equally important.
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