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In the book The elements of statistical learning by Trevor Hastie, there is a sentence (on page 17) saying :

In fact 1-nearest-neighbor, the simplest of all, captures a large percentage of the market for low-dimensional problems.

I am just very curious, in which circumstances is 1-nearest-neighbor used often?

You can get the book here.

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  • $\begingroup$ Other one-nearest-neighbor procedures typically have words like "voronoi," "thiessen," and "polygons of influence" in their names. They are frequently the basis of many maps, especially choropleth maps, whose data are originally measured at points. Arguably, many procedures involving binning of data are 1-NN or closely akin to it. $\endgroup$ – whuber Mar 1 '16 at 20:32
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I have seen it used for prediction of multiple (very many) responses in missing data imputation.

In this particular case, I think 1-nearest-neighbor is potentially a more elegant solution than the prediction of thousands of variables via (for example) a neural network.

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