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How exactly does it differentiate between a local and global structure in data?

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The core idea is to define distance-based probability estimates for a point. If two points are close, their Euclidean distance will be small. Thus, they will have a higher probability of being neighbors (this contributes to local structure).

Local and global structure part is, in fact, not paywalled in the full article so you can understand better with visuals here: https://www.dailydoseofds.com/formulating-and-implementing-the-t-sne-algorithm-from-scratch/.

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