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What does it mean to have a good PLS-DA model (in terms of both sensitivity and specificity on independent test set), but very noisy loadings (the data is IR spectrum, and it lost its spectral shape in the loadings at least for the 1st couple of factors, making it very difficult to interpret)? I have noticed that this noise is attributed to standard deviation weighting and the narrow point spacing, but those were associated with better performance, so I was just wondering if this noise is a critical error that I should compromise the model performance to avoid.

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IR spectrum is one of those highly multicollinear data types meaning that the variables are linearly similar behaving. Considering the Gaussian shape of the IR signals (peaks) that makes up the entire spectrum, this is no surprise.

Unfortunately, this inevitable multicollinearity issue is what makes the loadings look "noisy". Let's say an IR peak is related to the class information, there isn't much to do to differentiate which part of the peak is particularly related(assuming no peak overlap for thought exercise purposes). When the noise is also taken into account the interpretation of loadings problem get even worse.

All in all, in my opinion model performance is what matters most for such data. However, if you are particularly chasing interpretation and can obtain interpretable loadings with small model performance compromise, I think it's OK too.

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  • $\begingroup$ Thank you for the elaboration. Any suggestions about determining the important wavenumbers for the model using these noisy loadings? $\endgroup$ – elkadi Nov 1 '20 at 17:35

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