[seanhunter]

Yeah there are a few other ways. The most common are the “L2 norm”, which would be the hypoteneuse of a right triangle. so if your points are (x1,y1), (x2,y2) then it is sqrt((x1-x2)^2 + (y1-y2)^2)) which you might recognise from Pythagoras’ theorem (c^2 = a^2 + b^2). If you have 1000 dimensions then instead of just twice for x and y you are doing that that a thousand times but the principle is the same.

Another one is “Manhattan distance” (known as the L1 norm or sometimes as “taxicab distance”), which is just abs(x1-x2)+abs(y1-y2) in that example. If you imagine a set of city blocks and you want to go from one place to another the cab has to go north/south and east/west and can’t go diagonally. That’s the distance it travels. You’re adding up all the North/south parts and the east/west parts.

There are a bunch of other distance measures eg one project I worked on we used Mahalanobis distance which is a more complex measure which adjusts for dimensions in your space being affected by covariance. That wouldn’t be useful for this particular problem though.