Welcome back. It is often the case that you'll end up having vectors in very, very high dimensions. You want to find a way to reduce the dimension of these vectors to two dimensions so you can plot it on an XY axis. You will now learn about principal components analysis, which will allow you to do so. You are going to be using principal component analysis to visualize vector representations with higher dimensions than the ones that you've seen plotted so far. To get started, I'll give you some intuition on the motivation for visualizing vector presentation of words. And you'll see for yourself what principal components analysis does and how it is used for dimensionality reduction. Imagine you have the following representation for your words in a vector space. In this scenario, your vector space dimension is higher than tw. You know that the words oil and gas, and city, and town are related. And you want to see if that relationship is captured by the representation of your words. So how could you visualize your words in order to see this and other possible relationships? Dimensionality reduction is a perfect choice for this task. When you have a representation of your words in a high dimensional space. You could use an algorithm like PCA to get a representation on a vector space with fewer dimensions. If you want to visualize your data, you can get a reduced representation with three or fewer features. If you perform principal components analysis on your data and get a two-dimensional representation, you can then plot a visual of your words. In this case, you might find that your initial representation captured the relationship between the words oil and gas, and city, and town. Because in your two-dimensional space they appear to be clustered with related words. You can even find other relationships among your words that you didn't expect, which is a fun and useful possibility. Now that you know what PCA can help you achieve, let's go into detail on how it works. For the sake of simplicity, I'll begin with a two dimensional vector space. Say that you want your data to be represented by one feature instead. Using PCA, first you'll find a set of uncorrelated features. And then projects your data to a one dimensional space, trying to retain as much information as possible. As you can see, this process is quite straightforward. Coming up, you'll see for yourself the details of how this algorithm works. Along with how to get uncorrelated features, you'll also project your data for your representation in a lower dimension while retaining as much information as possible. Let's do a quick review before you go. PCA is an algorithm used for dimensionality reduction that can find uncorrelated features for your data. It's very helpful for visualizing your data to check if your representation is capturing relationships among words.