R Tutorial: The importance of scale

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. --- When calculating the distance between two players on a soccer field, you used two features, x and y. Both of these features are the coordinates of the players and both are measured in the same manner. Because of this, they are comparable to one another and can be used together to calculate the euclidean distance between the players. But, what happens when the features aren't measured in the same manner or to put it another way, when the values of these features aren't comparable to one another? To answer this question let's walk through an example. Imagine you are provided with a dataset that contains the heights and weights for a large number of men in the United States. The height feature is measured in feet and the weight feature in pounds. You are interested in calculating the distance between these individuals. Let us start by comparing observations one and two. Both men are the same height, six feet. But they differ slightly in weight. In this case the difference is two pounds. If we calculated the euclidean distance between them we would get a value of two. Now let's look at observations one and three. In this comparison, the weights are the same, but the height is different by two feet. If we calculate the distance once more... ...you guessed it. It's also two. The distances between both pairs are identical. If we saw these three men standing side by side, would you really believe that observation one is just as similar to three as it is to two? Of course not. Then why are their distances the same? This happens because these features are on different scales. Meaning they have different averages and different expected variability. While in these comparisons these features only vary by a magnitude of two, we intuitively know that