The problematic projection into vectors is done using a window size of a constant number of samples? Isn't that very weird?

Unless the samples are nicely periodic, that makes the contents of a vector, and the position of a value in a vector, dependent only on the window length and the order of time values, and not the time values themselves. Since the ordering in the vector, and thus the meaning of that dimension in vector space, is likely to be effectively random, why would we expect clustering in that vector space to mean anything? It's a weird thing to do on the face of it.