# RMSE behaviour during cross-validation of a PLS model - What does it mean?

In PLS regression, one of the approaches in selecting the number of components (Latent Variables, LV) is to perform cross-validation over a range of LV, and select the one with lower Root Mean Squared Error ($$RMSE_{CV}$$). I have tried this approach and until now, when I plotted $$RMSE_{CV-train}$$ and $$RMSE_{CV-test}$$, there is a number of LVs where $$RMSE_{CV-test}$$ reach a minimum and then start increasing again, while $$RMSE_{CV-train}$$ keeps decreasing. This implies the overfitting of the model. In the previous implementations I have done, the value of LVs for the minimum $$RMSE_{CV-test}$$ is between 5 and 15.

Now, I am testing the same in a new dataset and when plotting the same graph for 4 different models (and dependent variables), found some "unusual" behaviours:

• In 2 of the cases, the minimum $$RMSE_{CV-test}$$ is using just 2 Latent variable (Prop. 0 and Prop. 3)
• In the other 2 cases, $$RMSE_{CV-test}$$ start increasing from the beginning (Prop. 1 and Prop. 2)

I have never seen this kind of evolution in the RMSE of a PLS model based on the number of Latent Variables used.

This dataset consists of 128 features (columns) and 59 samples (rows), and there are 4 output variables (Prop 0 to Prop. 3 in the graph)

What does this behaviour mean or what could be its cause?