Remember when we were doing movie similarities and movie recommendations earlier in the book? An example of a vector might be a list of all the movies that a given user rated. There are two types of vector, sparse and dense. Let's look at an example of those. There are many, many movies in the world, and a dense vector would actually represent data for every single movie, whether or not a user actually watched it. So, for example, let's say I have a user who watched Toy Story, obviously I would store their rating for Toy Story, but if they didn't watch the movie Star Wars, I would actually store the fact that there is not a number for Star Wars. So, we end up taking up space for all these missing data points with a dense vector. A sparse vector only stores the data that exists, so it doesn't waste any memory space on missing data, OK. So, it's a more compact form of representing a vector internally, but obviously that introduces some complexity while processing. So, it's a good way to save memory if you know that your vectors are going to have a lot of missing data in them.