Are there any machine learning algorithms that focus on comparing items, rather than classification or regression? 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.
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.