The Grand Locus / Life for statistical sciences

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## A tutorial on t-SNE (3)

This post is the third part of a tutorial on t-SNE. The first part introduces dimensionality reduction and presents the main ideas of t-SNE. The second part introduces the notion of perplexity. The present post covers the details of the nonlinear embedding.

### On the origins of t-SNE

If you are following the field of artificial intelligence, the name Geoffrey Hinton should sound familiar. As it turns out, the “Godfather of Deep Learning” is the author of both t-SNE and its ancestor SNE. This explains why t-SNE has a strong flavor of neural networks. If you already know gradient-descent and variational learning, then you should feel at home. Otherwise no worries: we will keep it relatively simple and we will take the time to explain what happens under the hood.

We have seen previously that t-SNE aims to preserve a relationship between the points, and that this relationship can be thought of as the probability of hopping from one point to the other in a random walk. The focus of this post is to explain what t-SNE does to preserve this relationship in a space of lower dimension.

## A tutorial on t-SNE (1)

In this tutorial, I would like to explain the basic ideas behind t-distributed Stochastic Neighbor Embedding, better known as t-SNE. There are tons of excellent material out there explaining how t-SNE works. Here, I would like to focus on why it works and what makes t-SNE special among data visualization techniques.

If you are not comfortable with formulas, you should still be able to understand this post, which is intended to be a gentle introduction to t-SNE. The next post will peek under the hood and delve into the mathematics and the technical detail.

### Dimensionality reduction

One thing we all agree on is that we each have a unique personality. And yet it seems that five character traits are sufficient to sketch the psychological portrait of almost everyone. Surely, such portraits are incomplete, but they capture the most important features to describe someone.

The so-called five factor model is a prime example of dimensionality reduction. It represents diverse and complex data with a handful of numbers. The reduced personality model can be used to compare different individuals, give a quick description of someone, find compatible personalities, predict possible behaviors etc. In many...