Abstraction in Aristotle is sometimes made out to be mysterious. I think it is just straightforward subtraction of features of a thing that have been previously recognized as “accidental” for the pertinent context of evaluation. Abstraction is neither a way of magically laying bare the true inner essence of a thing, as envisioned by some medieval realists, nor the mental creation of a universal ex nihilo, as envisioned by some nominalists. It is also does not have any necessary dependency on induction.
What counts as accidental may vary with the context of evaluation. While distinctions of essence and accident are fairly stable within a given context, they are ultimately relative and contextual. The pertinent context includes not only contingent facts about what is being evaluated, but also the purpose of the evaluation.
In other, non-Aristotelian contexts, Badiou has recently made it somewhat fashionable to speak literally about “subtraction” instead of “abstraction”. Though I have many issues with his thought, this is actually a useful clarification.