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I was going through the t-SNE, but I am bit confused. While the original paper of t-SNE is based on the SNE and SNE uses $\sigma_i^2$ (note the subscript $i$) while calculating the similarity of point $x_i$ WRT other points j. i.e., for each data point $x_i$ the corresponding $\sigma_i^2$ is used. But t-SNE uses only $\sigma^2$ (not $\sigma_i^2$) while calculating the similarity of every data point centred at $x_i$. This is even mentioned in the original paper of t-SNE (below Equation 3). However, I found lot of resources on t-SNE that claim $\sigma_i^2$ for data point centred at $x_i$(not $\sigma^2$), which is completely contrary to what is used in the paper. However, I found this lecture https://youtu.be/4GBgqmq0XAY?t=2555 mentioning correctly the mathematics of t-SNE (as used in the original paper)

Can you kindly explain, what is actually going on?

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t-SNE calculates different sigma for each data point, thus the sigma should be indexed. See https://en.wikipedia.org/wiki/T-distributed_stochastic_neighbor_embedding for details.

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