I'm trying to capture what I am doing mathematically using a math formula / math notation. I've calculated the "Mean Per-Class Error (MPCE)" from a multi-class classification problem.
In words, the concept behind MPCE is as follows:
Per-class recall error = (members of class identified incorrectly)/(number of members of class)
Simply multiply each per-class recall error value by the number of samples that are actually in the class to get the number of each class classified correctly, add these up to get the total number of correct predictions, and then divide by the total number of samples to get the mean per-class error.
I need to convert the above words into a nifty math formula. How do I do that?
I think you are looking for a weighted average. See https://en.wikipedia.org/wiki/Weighted_arithmetic_mean
Your words are the formula you need. You can make it fancy (but no more "mathematical") with the official symbol $\Sigma$ for summation. $$ \text{MPCE} = \frac{\sum_\text{classes}\text{PCRE}\times\text{size of class}}{\sum_\text{classes} \text{size of class}} . $$