Unluckily I know little about homological algebra, algebraic topology and descriptive set theory. But I surely have already seen papers where methods from alge

Unluckily I know little about homological algebra, algebraic topology and descriptive set theory. But I surely have already seen papers where methods from algebraic topology are applied for pattern detection or finding whether some high-dimensional data are homeomorphic. Also simplicial complexes (that are used in homological algebra and algebraic topology) can also come from triangulating high-dimensional point sets (for example from big data). I could well imagine that methods from homological algebra or algebraic topology could give us some insight into some properties of this data.