Nonlinear dimensionality reduction

Nonlinear dimensionality reduction is a way to take a group of data points which have many different properties, and turn them into a smaller, simpler group of data points which still show all the same properties. It does this by looking at how the data points are related to each other and finding the simplest way to show all of those relationships. For example, if you had a group of data points that represented the height, weight, and shoe size of a bunch of people, it might be really hard to show all those pieces of information at once. But if you used nonlinear dimensionality reduction, you could make a map where each point was like a person's height and weight, and a line would show their shoe size. That way, you could easily show all the info in one simple picture.