# Chernoff Faces

We haven't had much on graphics on this blog yet, partly because there are several specialized fora for this peculiar aspect of statistics: for instance, junkcharts, the R-gallery, information aesthetics, the Statistical Graphics and Data Visualization blog, the Data Mining blog, Edward Tufte's forum, Andrew Gelman's blog and others. Yet, I assume readers of this blog wouln't mind a picture every once in a while, so here are some Chernoff faces for you right there. In spirit of Mike's recent entry, they illustrate team statistics from the 2005 baseball season:

I recently came across the Chernoff faces while looking for a neat way to display multivariate data to compare several cities along various dimensions in a single plot. Chernoff faces are a method introduced by Herman Chernoff (Prof Emeritus of Applied Math at MIT and of Statistics at Harvard) in 1971 that allows one to convert multivariate data to cartoon faces, the features of which are controlled by the variable values. So for example in the above graph, each teams winning percentage are represented by face height, smile curve, and hair styling; hits are represented by face width, eye height, nose height; etc. (for details and extensions see here).

The key idea is that human are well trained to recognize faces and discern small changes without difficulty. Therefore Chernoff faces allow for easy outlier detection and pattern recognition despite multiple dimensions of the data. Since the features of the faces vary in perceived importance, the way in which variables are mapped to the features should be carefully chosen.

Mathematica and R have canned algorithms for Chernoff faces (see here and here). I haven't seen a Chernoff plot in a social science journal yet, but maybe I am reading the wrong journals. Does anyone know articles that use this technique? Also do you think that this is an effective way of displaying data that should be used more often? Obviously there are also problems with this type of display, but even if you don't like the key idea you have to admit that they look much funnier then the boring bar-graphs or line plots we see all the time.

Posted by Jens Hainmueller at November 10, 2006 10:29 AM