How to interpret balances after ILR transform for compositional data?

I have a dataset with rows of compositional data representing character preferences (~150 characters), essentially the percentage of time played as a specific character. I would like to get correlations between the characters to eventually make recommendations. From what I understand the approach for compositional data is to apply an ILR transform and then deal with the balances in the new space. All examples I have found so far have relied on some predefined hierarchy/tree to interpret the resulting balances but this is not the case here, how should I go about this?