If you massage the four data points to be part of a curve and then analyze that curve with Fourier transform, you can make an Andrews plot. It turns out this isn’t much better or worse than the Parallel Coordinates depiction:

Once again, the main conclusion you can draw is that the green bits are different from everything else, and the orange and purple bits are similar.

If you used polar coordinates — i.e. if you took the bottom x-axis and bent both ends around to form a triangle or a circle, you’d get a radar or star plot or something similar.

If you are like me, you are probably thinking that Parallel Coordinates and related techniques aren’t exactly easy to understand or interpret.

But there are other ways of representing dimensions. A triangle, for instance, could be used to represent three dimensions of data, if you mapped each dimension to the length of a side. You could, if you really wanted, utilize a red-blue spectrum and a light-dark spectrum to color in the middle of the triangles and blamo! You’ve got five continuous dimensions all in one. Compare each triangle, and you might spot anomalies or heretofore hidden patterns and relationships. That’s the theory, anyways.

It turns out that a researcher named Paul Chernoff explored a variant of this idea in the 1970s — instead of lengths of triangle-sides, he mapped dimensions of data to different characteristics of cartoon faces.

I’ll let you judge how well this worked by way of L.A. Times infographic:

Eugene Turner — Life in Los Angeles (1977), L.A. Times. The four facial dimensions, the geographic distribution of each face and the community-line information mean you are looking at six dimensions of data.

Your gut reaction will be to dismiss this method of data presentation, as it looks silly, vaguely racist, and hard to interpret. But I urge you to give it a second look — can you spot the buffering row of communities in between the poor and affluent parts of town?

One reason Chernoff faces don’t get wider use, I submit, is that they look too cartoonish. (And seeing how science is very Serious Business, it wouldn’t be proper for plots to be cartoon faces…)

While realistic Chernoff faces solve the cartoonishness problem, they highlight another issue: though they seem like they could be intuitive, we all have too much experience with faces and real emotions to evaluate arbitrarily constructed ones.

In the depictions below, parameters of Tim Cook’s face — like the slope of his eyebrows — have been mapped to various Apple financial data-points for the year in question.

From Christo Allegra. Each version of Tim Cook’s face represents Apple’s financial data for the year in question. The width of Tim Cook’s nose represents the amount of debt taken on by Apple; the closed-ness of Cook’s mouth represents the revenue of that year; the size of his eyes represents the earnings per share, and so on. For serious uses of Chernoff faces, check out Dan Dorling’s work.

Clearly, there are some issues with this approach too. One thing that stands out is that not every aspect of a face conveys emotional information on the same scale as, for instance, the smile.

In other words, the perceptual difference between one face and another doesn’t match the actual differences between the data.

This, I submit, is one of the properties that makes plots and graphs so useful, and something that is missing from current approaches high-dimensional data visualization.