•

the Blog

## A tutorial on t-SNE (2)

By Guillaume Filion, filed under
perplexity,
t-SNE,
entropy.

• 16 December 2019 •

In this post I explain what perplexity is and how it is used to parametrize t-SNE. This post is the second part of a tutorial on t-SNE. The first part introduces dimensionality reduction and presents the main ideas of t-SNE. This is where you should start if you are not already familiar with t-SNE.

### What is perplexity?

Before you read on, pick a number at random between 1 and 10 and ask yourself whether I can guess it. It looks like my chances are 1 in 10 so you may think “no there is no way”. In fact, there is a 28% chance that you chose the number 7, so my chances of guessing are higher than you may have thought initially.
In this situation, the random variable is *somewhat predictable but not completely*. How could we quantify that?

To answer the questions, let us count the possible samples from this distribution. We ask $(N)$ people to choose a number at random between 1 and 10 and we record their answers $((x_1, x_2, \ldots, x_N))$. The number 1 shows up with probability $(p_1 = 0.034)$ so the total in the sample is approximately $(n_1...