Spotting Differences - Data Points: Visualization That Means Something - page 259

the connecting lines, so it'd be nice if you could cluster objects, based on
several criteria. This is one of the goals of multidimensional scaling (MDS).
Take everything into account, and then place units that are more similar
closer together on a plot.

P For more
details on the
method, look up
multidimensional
scaling or princi-
pal components
analysis.

entire topics are written on this topic, so explanations can get technical,
but for the sake of simplicity, I'll keep it at a high level and leave the math
for another day. That said, MDS is one of the first concepts I learned in
graduate school, and it is worth learning the mechanics behind it, if you're
into that sort of thing.

Imagine that you're in an empty, square-shaped room and there are two
other people there. It's your job to tell those people where to stand in the
room, based on their height. The more similar their height, the closer they
should stand, and the more different their height, the farther away they
should stand. One is really short. The other is really tall. Where should
they go? The two people should stand at opposite corners, because they
are complete opposites.

Now a third person comes in, and he's medium height. Sticking with the
arrangement scheme, the new person should stand in the center of the
room, right in between the first two. He's equally different from the tall
and the short, so he's equal distance from each. At the same time, the tall
and short people are still maximum distance from each other.

Okay, now introduce another variable: weight. You know the height and
weight of all three people. The short and medium height people are actu-
ally the exact same weight whereas the tall person is, say, a third heavier.
How can you, based on height and weight, place the three people in the
room? Well, if you keep the first two people (short and tall) in their oppo-
site positions, the third person (medium height) would need to move closer
to the shorter person, because their weights are the same.

Do you get what is occurring? The more similar two people are, the
closer they should stand to each other. In this simple case, you have only
three people and two variables, so it's easy to work this out manually,
but imagine you have 50 people, and you have to place them in the room
based on say, five criteria. It's trickier. And that's what multidimensional
scaling is for.