Calculating the Distance to the Centroid

We've talked a lot about similarities between data points in the previous sections, but we haven't really defined what this means. You have probably guessed that it has something to do with how close or how far observations are from each other. You are heading in the right direction. It has to do with some sort of distance measure between two points. The one used by k-means is called squared Euclidean distance and its formula is:

Figure 5.32: The squared Euclidean distance formula

If you don't have a statistical background, this formula may look intimidating, but it is actually very simple. It is the sum of the squared difference between the data coordinates. Here, x and y are two data points and the index, i, represents the number of coordinates. If the data has two dimensions, i equals 2. Similarly, if there are three dimensions, then i will be 3.

Let's apply this formula to the ATO dataset....