R Tutorial: Distance between two observations

Want to learn more? Take the full course at https://learn.datacamp.com/courses/cluster-analysis-in-r at your own pace. More than a video, you'll learn hands-on coding & quickly apply skills to your daily work. --- Let's begin by focusing on the question that is fundamental to all clustering analyses: How similar are two observations? Or from another perspective, how dissimilar are they? You see, most clustering methods measure similarity between observations using a dissimilarity metric often referred to as the distance. These two concepts are just two sides of the same coin. If two observations have a large distance then they are less similar to one another. Likewise, if their distance value is small, then they are more similar. Naturally, we should first develop a keen intuition by what is meant by distance. So, let's work with the scenario of players on a soccer field. In this image, you see the positions of two players. How far apart are they? To answer this question we first need their coordinates. Here the blue player is positioned in the center of the field, which we will refer to as 0, 0. While the red player has a position of 12 and 9 - or twelve feet to the right of center and 9 feet up. The players, in this case, are our observations and their X and Y coordinates are the features of these observations. We can use these features to calculate the distance between these two players. In this case, we will use a distance measurement you're likely familiar with. Euclidean distance which is simply the hypotenuse of the triangle that is formed by the differences in the x and y coordinates of these players. The familiar formula to calculate this is shown here. Which if we plug in our values of x and y for both players we arrive at the euclidean distance between them. Which in this case is 15? This is the fundamental idea for calculating a measure of dissimilarity between the blue and red players. To do this in R, we use the dist function to calc