Hi @ravibot,
You can refer to this post here where you can access the formulae: Variance of the VIP statistics from PLS
The VIP measures the importance of the variables to explain the variance related to the predictors (typically the X data set), whereas the loading weights are the direct regression coefficients used to define the latent components (to maximise the covariance between data sets X and Y).
We do not consider PLS-DA as a ‘regression’ method given that it performs classification, but the VIP is still implemented for this method. We typically use the loading vectors, especially when using a sparse method where variable selection is performed. (I did some test previously and some selected variables that are the least important may lead to a VIP <1).
Kim-Anh