R Tutorial: PCA and t-SNE

Want to learn more? Take the full course at https://learn.datacamp.com/courses/advanced-dimensionality-reduction-in-r at your own pace. More than a video, you'll learn hands-on coding & quickly apply skills to your daily work. --- In the previous lesson, we discussed distance metrics and their application to find similar objects in a feature space. It's clear that the task of finding similar digits based on their pixel features is a complex task and can't be easily solved using distance metrics. One of the problems of distance metrics is their inability to deal with high-dimensional datasets, which is known as the curse of dimensionality. In this lesson, we will explain the curse of dimensionality concept and then focus on how the problem of finding similar digits can be solved using dimensionality reduction techniques such as PCA and t-SNE, which usually provides better results than PCA. One of the issues of finding similar objects in high dimensional spaces that does not occur in low dimensional ones (for example in three dimensions), is the curse of dimensionality. The term was coined by Richard Bellman. It describes the phenomena that arise when the number of dimensions grows, making the volume of the space increase so fast, requiring an exponential amount of data to preserve the previous distance in lower dimensions. For instance, in this example, you can see that we can capture 37.5% of the points in one dimension for a distance of 0.4. If we keep the same distance we will only cover 10% of the points in two dimensions. And the same effect happens in higher dimensions. One way to avoid this effect is using dimensionality reduction techniques. PCA is one of the most classic and well-known dimensionality reduction techniques. As you know, it has been covered in a previous dimensionality reduction course at DataCamp. PCA is a linear feature extraction technique. It creates new independent features by maximizing the variance of the data in the new lo