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So let's take a look at how we can develop a recommended system if we had features of each item, or features of each movie. So here's the same data set that we had previously with the four users having rated some but not all of the five movies. What if we additionally have features of the movies? So here I've added two features X1 and X2, that tell us how much each of these is a romance movie, and how much each of these is an action movie. So for example Love at Last is a very romantic movie, so this feature takes on 0.9, but it's not at all an action movie. So this feature takes on 0. But it turns out Nonstop Car chases has just a little bit of romance in it. So it's 0.1, but it has a ton of action. So that feature takes on the value of 1.0. So you recall that I had used the notation nu to denote the number of users, which is 4 and m to denote the number of movies which is 5. I'm going to also introduce n to denote the number of features we have here. And so n=2, because we have two features X1 and X2 for each movie. With these features we have for example that the features for movie one, that is the movie Love at Last, would be 0.90. And the features for the third movie Cute Puppies of Love would be 0.99 and 0. And let's start by taking a look at how we might make predictions for Alice's movie ratings. So for user one, that is Alice, let's say we predict the rating for movie i as w.X(i)+b. So this is just a lot like linear regression. For example if we end up choosing the parameter w(1)=[5,0] and say b(1)=0, then the prediction for movie three where the features are 0.99 and 0, which is just copied from here, first feature 0.99, second feature 0. Our prediction would be w.X(3)+b=0.99 times 5 plus 0 times zero, which turns out to be equal to 4.95. And this rating seems pretty plausible. It looks like Alice has given high ratings to Love at Last and Romance Forever, to two highly romantic movies, but given low ratings to the action movies, Nonstop Car Chases and Swords vs Karate. So if we look at Cute Puppies of Love, well predicting that she might rate that 4.95 seems quite plausible. And so these parameters w and b for Alice seems like a reasonable model for predicting her movie ratings. Just add a little the notation because we have not just one user but multiple users, or really nu equals 4 users. I'm going to add a superscript 1 here to denote that this is the parameter w(1) for user 1 and add a super strip 1 there as well. And similarly here and here as well, so that we would actually have different parameters for each of the 4 users on data set. And more generally in this model we can for user j, not just user 1 now, we can predict user j's rating for movie i as w(j).X(i)+b(j). Only now we're training a different linear regression model for each of the nu users. So that's how you can learn parameters and predict movie ratings, if you had access to these features X1 and X2. That tell you how much is each of the movies, a romance movie, and how much is each of the movies an action movie? But where do these features come from? And what if you don't have access to such features that give you enough detail about the movies with wish to make these predictions? In the next video, we'll look at the modification of this algorithm. They'll let you make predictions that you make recommendations. Even if you don't have an advanced features that describe the items of the movies in sufficient detail to run the algorithm that we just saw. Let's go on and take a look at that in the next video

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