This question is a follow-up to this one and is about Magic: the Gathering decks, specifically in the EDH/Commander (singleton) format:
I have a group of samples (decks), each one consisting of 100 nominally categorical datapoints (cards). Each sample is aggregated by an individual (deck builder), e.g. it's known that these are not random collections of datapoints.
The linked question is regarding how to quantitatively determine similarity between decks, but I think I need to take a step back: I want to take a subset of all the decks there are and analyze it; specifically, I want to select the subset that share a "commander" (a single card that represents how the deck is constructed) and classify them according to archetype, where an archetype is defined as some feature about how the deck operates/wins. An archetype manifests itself in the same sorts of cards being included in decks of that archetype. As an illustration, one archetype might be made up of decks that include at least 30% of a pool of 40 cards; not every deck in that archetype has all of the cards, but they all are doing more or less the same thing.
Given a subset of categorical nominal data that has some unifying aspect, does there exist a method to algorithmicaly identify classifications?