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I wonder how this stuff copes with very noisy data.
Pretty well in my experience - A few years ago I used it with Illumina data obtained from in vivo phage display.
By chance, does anyone have any immediate resources to learn more about topology? I've been interested in applying it to my work, but as a topic it's rather "out there" so to speak, so it's difficult to find relevant introductory material.
Afra Zomorodian has a pretty accessible book called 'Topology for Computing'.

You can also play around with OSS such as pymapper, jplex etc.