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According to the triplet loss Wikipedia page:

t-SNE (t-distributed Stochastic Neighbor Embedding) preserves embedding orders via probability distributions, whereas triplet loss works directly on embedded distances.

I don't understand how does t-SNE preserves embedding order from the description given by its Wikipedia page.

I am trying to understand this claim in order to translate the page into other languages. I don't have a very quick understanding of maths, don't be afraid to explain it as if I was a teenager.

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You just to look at the method of T-SNE. It "computes probabilities $p_{ij}$ that are proportional to the similarity of objects ${x} _{i}$ and ${x} _{j}$". This means the same as the sentence that you have already quoted:

t-SNE (t-distributed Stochastic Neighbor Embedding) preserves embedding orders via probability distributions, whereas triplet loss works directly on embedded distances.

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