Dimensionality reduction and principal component analysis

Alright, time to get all trippy! We're going to talking about higher dimensions, and dimensionality reduction. Sounds scary! There is some fancy math involved, but conceptually it's not as hard to grasp as you might think. So, let's talk about dimensionality reduction and principal component analysis next. Very dramatic sounding! Usually when people talk about this, they're talking about a technique called principal component analysis or PCA, and a specific technique called singular value decomposition or SVD. So PCA and SVD are the topics of this section. Let's dive into it!

Dimensionality reduction

So, what is the curse of dimensionality? Well, a lot of problems can be thought of having many different dimensions. So, for example, when we were doing movie recommendations, we had attributes of various movies, and every individual movie could be thought of as its own dimension in that data space.

If you have a lot of movies, that's a...