Distance Metric Learning benchmark datasets.
The dataset must possess the four properties of a metric space: (1) the non-negativity axiom; (2) the identity of discernibles; (3) symmetry; and (4) the triangle inequality. Look up "metric space" in the internet.
Refer to the following research article.
https://www.cs.cmu.edu/~liuy/frame_survey_v2.pdf
http://jmlr.csail.mit.edu/papers/volume10/weinberger09a/weinberger09a.pdf
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