{"id":807,"date":"2026-08-17T17:57:38","date_gmt":"2026-08-17T09:57:38","guid":{"rendered":"https:\/\/www.toothlessos.xyz\/?p=807"},"modified":"2026-08-17T17:57:42","modified_gmt":"2026-08-17T09:57:42","slug":"t-sne-in-50-lines-of-code-with-pytorch","status":"publish","type":"post","link":"https:\/\/www.toothlessos.xyz\/index.php\/2026\/08\/17\/t-sne-in-50-lines-of-code-with-pytorch\/","title":{"rendered":"t-SNE in 50 lines of code with PyTorch"},"content":{"rendered":"\n\n\n

t-SNE is one of the most popular dimensional reduction<\/strong> techniques for visualizing high-dimensional data. It preserves the local structure<\/strong> in the high-dimensional dataset – In other words, similar data points that are close to each other should still be close to each other after dimension reduction. One classic example here is applying t-SNE on the MNIST hand-written digits dataset, where we can find nice clusters for each of the digits:<\/p>\n\n\n\n

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Different digits form different clusters after t-SNE, illustrating that t-SNE successfully preserves the local structure of the original dataset. Figure taken from: t-SNE-Mnist-Dataset<\/a><\/figcaption><\/figure>\n\n\n\n

This ToothlessOS Log provides a demo explanation of t-SNE with step by step walk through to help you better understand this beautiful algorithm.<\/p>\n\n\n\n\n\n

Intuition behind t-SNE<\/h2>\n\n\n\n

Given a dataset \"X\", t-SNE builds a probability distribution \"P\" over pairs of high-dimensional data points. Then, it learns a low dimensional embedding \"Y\" by minimizing the KL-divergence between \"P\" and a low-dimensional distribution \"Q\". Personally, the keywords that I keep for t-SNE is pairwise distances<\/strong> and matching probability distributions<\/strong>, which we will walk through in the next section. I find it very helpful to use such keywords to capture the objectives<\/strong> of dimensional reduction algorithms – to make sure that I use them properly in practice.<\/p>\n\n\n\n

Implementation walkthrough<\/h2>\n\n\n\n

Step 1: Pairwise squared distances<\/h3>\n\n\n\n
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