This is more of a hypothetical than something I'm actively trying to solve. It just struck me that a machine learning algorithm that specifically looked at two pieces of data and had to label one as greater than the other or something of that nature might be inherently different than classifying each separately and comparing the strength of the classifications.

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    Isn't this just like binary classification? 0 for first item equal or greater than the second item, otherwise 1? Why can't you do a binary (or k=3) classification? – SmallChess Nov 7 '15 at 2:51
  • I'm not saying you can't, but implicitly you're measuring how one piece of data fits in with all the other data the algorithm has seen. Perhaps you only care about the difference between two pieces of data. I guess you could derive some features using proportions and differences. But already that's different from simply doing binary classification. And what if I know that in a given pair exactly one of them is 1 and the other is 0? Perhaps the way I'm paring the data matters because the two pieces of data aren't independently drawn. – Ram Nov 7 '15 at 2:57
  • What would you do with this direct comparison? What would greater than mean? – paparazzo Nov 7 '15 at 16:44
up vote 6 down vote accepted

There are ranking algorithms based on machine learning that are aimed to build ranking models. Training data for these models is given in the form of partial ordering between each pair of elements in a sample. A brief description, together with a list of useful references, is given in the corresponding Wikipedia page.

  • Ah, yes. I think this is probably the right way of thinking about it, a partial ordering. It looks like a fun little rabbit hole to go down. Thanks. – Ram Nov 21 '15 at 0:56

Not sure if I read the question correctly, but I have implemented multi-variate sub-sample optimisation routines using the Kolmogrov-Smirnov test?

The advantage is that if two distributions exactly track each other (so would be significantly correlated) but are at quite different scales (e.g. one is half the value of the other), they would still rank as very different distributions at similar scales. Only when both distribution and scale match is the ranking high.

Spatially per-pixel comparison algorithms are also quite common in raster analysis?

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