I have data I want to analyze using multiple regression or machine learning: the response is cells for which I measured viability (a continuous response) and the independent variables are the genes in the genome where each can have 21 types of mutations. In other words, each gene is a categorical factor with 21 levels. The thing is that while 90% of the genes have only a single type of mutation the remaining 10% have multiple types of mutations. So in practice there are 612 combinations of mutations. One option is to have the 21 mutation types for each gene as a binary factor, meaning I'll have 20,000*21 = 420,000 factors. Another option is to have 612 levels for each of the 20,000 genes.
Which option is better given that I only have 500 cells and are there better options than those two?