# Chernoff face

Chernoff faces, invented by applied mathematician, statistician and physicist Herman Chernoff in 1973, display multivariate data in the shape of a human face. The individual parts, such as eyes, ears, mouth and nose represent values of the variables by their shape, size, placement and orientation. The idea behind using faces is that humans easily recognize faces and notice small changes without difficulty. Chernoff faces handle each variable differently. Because the features of the faces vary in perceived importance, the way in which variables are mapped to the features should be carefully chosen (e.g. eye size and eyebrow-slant have been found to carry significant weight).[1]

## Detail

Chernoff faces themselves can be plotted on a standard XY graph; the faces can be positioned XY based on the two most important variables, and then the faces themselves represent the rest of the dimensions for each item. Edward Tufte, presenting such a diagram, says that this kind of Chernoff-face graph would "reduce well, maintaining legibility even with individual areas of 0.05 square inches as shown ... with cartoon faces and even numbers becoming data measures, we would appear to have reached the limit of graphical economy of presentation, imagination, and let it be admitted, eccentricity".[2]

## Extensions

### Asymmetrical faces

In 1981, Bernhard Flury and Hans Riedwyl suggested "asymmetrical" Chernoff faces;[3] since a face has vertical symmetry (around the y axis), the left side of the face is identical to the right and is basically wasted space – a point also made by Tufte.[4] One could have the 18 variables that specify the left be one set of data, but use a different set of data for the right side of the face, allowing one face to depict 35 different measurements. They present results showing that such asymmetrical faces are useful in visualizing databases of identical twins, for example, and are useful in grouping as pairs of Chernoff faces would be.[3]

### Chernoff fish

Julie Rodriguez and Piotr Kaczmarek use "Chernoff fish", where various parts of a cartoon fish are used to encode different financial details.[5]

## In literature

In Peter Watts' novel Blindsight (2006), a transhuman character is seen using a variant of Chernoff faces. This is explained by the character as a more efficient method of representing data, as a large portion of the human brain is devoted to facial recognition. [6]

In the 2014 sci-fi short story "Degrees of Freedom" by Karl Schroeder, Chernoff faces make a prominent appearances as a future technology, supporting the communication of aggregate sentiment and perspective.[7]

## References

1. ^ "An Experimental Analysis of the Pre-Attentiveness of Features in Chernoff Faces", Morris CJ, Ebert DS, Rheingans P. 1999; published by the conference "Applied Imagery Pattern Recognition: 3D Visualization for Data Exploration and Decision Making". http://www.research.ibm.com/people/c/cjmorris/publications/Chernoff_990402.pdf doi:10.1117/12.384865
2. ^ Edward R. Tufte, The Visual Display of Quantitative Information, p. 142.
3. ^ a b Flury, Bernhard; Riedwyl, Hans (December 1981). "Graphical Representation of Multivariate Data by Means of Asymmetrical Faces". Journal of the American Statistical Association. 76 (376). American Statistical Association: 757–765. doi:10.2307/2287565. JSTOR 2287565.
4. ^ Edward R. Tufte, The Visual Display of Quantitative Information, p. 97: "Halves may be easier to sort (by matching the right half of an unsorted face to the left half of a sorted face) than full faces. Or else an asymmetrical full face can be used to report additional variables (Flury & Riedwyl 1981). Bilateral symmetry doubles the space consumed by the design in a graph, without adding new information."
5. ^ Visualizing Financial Data. John Wiley & Sons. 2 May 2016. ISBN 9781118907856.
6. ^ Peter Watts. "Blindsight". Retrieved 2021-04-19.
7. ^ Karl Schroeder. "End notes from Karl Schroeder's "Degrees of Freedom"". Archived from the original on 2018-03-24. Retrieved 2018-03-23.