Welcome to KnowledgeCity's course on machine learning, and supervised machine learning methods. In these lessons, you'll learn about Gaussian mixture models, clustering, including k-means, DB scan, and optics, and manifold learning, including isomap, multi-dimensional scaling, and t-distributed stochastic neighbor embedding. This lesson is going to be on Gaussian mixture models where you'll learn what is a Gaussian mixture model, how are they used and how are they implemented? The Gaussian mixture model is a type of probabilistic model that assumes all points within a data set are generated from a finite number of Gaussian distributions. It can be viewed as a way of clustering your data in such a way that each cluster has a Gaussian distribution. This will make it possible to identify which cluster an unknown point belongs to with a high level of confidence. How are Gaussian mixture models used? Typically, they're used to represent normally distributed subpopulations within an overall population. They also are capable of automatically learning subpopulations without having any indication of which subpopulation a particular point may belong to. Next, we're going to get into how Gaussian mixture models are implemented in Python. This is using the scikit-learn package, and here, I'm going to show a clustering example, and then I'm going to show you how the distributions look for each of the clusters. So all I'm doing here is importing my packages, and then I'm creating a data set of noisy circles, which you'll see exactly what that looks like shortly. So what we have here are two circles. They're just made up of, you know, 5,000 points total. And here, I'm defining the mixture model. And for n components here, it's just the number of components, and so basically what that means is, because I'm using it as a clustering technique here, there are going to be two clusters or two subpopulations that are detected or defined. So now that that's done, I'm going to plot the two clusters. And so, as you can see here, the Gaussian mixture model separated the circles diagonally here, instead of an inner circle and outer circle. And so now that we have this, I just want to show you... A comparison. So, here we have the full population data, and then here we have the subpopulation data. So the idea here is that because this is a Gaussian mixture model, the model did its best so that the data that is blue and the data that's green both have Gaussian distributions. And so to check that, I'm going to plot those distributions. And so, as you can see here, both distributions are the same. In fact, they're just reflections of one another, and they're not perfectly Gaussian, but they do have the general shape of a Gaussian distribution. And so, two things to know about this. One, the data wasn't actually Gaussian distributed, right? And so, what the algorithm did was take the best, you know, split of the data, or, you know, cluster of the data that would get it as close to the Gaussian distribution as possible. If this data was actually Gaussian distributed, or even if we had more points, these plots would look more like the Gaussian distribution curves that we're used to seeing. So this concludes this lesson, and next up, we're going to discuss clustering. Thank you.