I have a **multiclass classification problem** (eg. the target variable is made by 4 different outcomes: Product A, Product B, Product C and NO Product). **Not all the errors are equal:** for example, if the true label is "Product A" and the prediction is "NO Product" it is not a big problem, while if the true label is "Product C" the impact of the error is much bigger. Basically, I have to insert this information into the loss function of the algorithm (I am currently using Xg-Boost, Random Forest, etc).

I know that it's possible, for example using `scikit-learn` to train algorithms using the parameter `class_weight` in a way that a specific class error is more important.

Is there the possibility to say, for example, that a miss-classification of product C in Product B is more problematic w.r.t a miss-classification of Product C to Product B? **I am basically looking at something that penalize the model for making cross predictions.**

Any idea? Thank you!