
Chernoff faces, invented by applied mathematician, statistician and physicist
Herman Chernoff
Herman Chernoff (born July 1, 1923) is an American applied mathematician, statistician and physicist. He was formerly a professor at University of Illinois Urbana-Champaign, Stanford, and MIT, currently emeritus at Harvard University.
Early ...
in 1973, display
multivariate
Multivariate may refer to:
In mathematics
* Multivariable calculus
* Multivariate function
* Multivariate polynomial
In computing
* Multivariate cryptography
* Multivariate division algorithm
* Multivariate interpolation
* Multivariate optical c ...
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
An eyebrow is an area of short hairs above each Human eye, eye that follows the shape of the lower margin of the Supraorbital ridge, brow ridges of some mammals. In humans, eyebrows serve two main functions: first, human communication, communica ...
-slant have been found to carry significant weight).
Detail
Chernoff faces themselves can be plotted on a standard ''X''–''Y'' graph; the faces can be positioned ''X''–''Y'' based on the two most important variables, and then the faces themselves represent the rest of the dimensions for each item.
Edward Tufte
Edward Rolf Tufte (; born March 14, 1942), sometimes known as "ET",. is an American statistician and professor emeritus of political science, statistics, and computer science at Yale University. He is noted for his writings on information desig ...
, 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".
Extensions
Asymmetrical faces
In 1981, Bernhard Flury and Hans Riedwyl suggested "
asymmetrical
Asymmetry is the absence of, or a violation of, symmetry (the property of an object being invariant to a transformation, such as reflection). Symmetry is an important property of both physical and abstract systems and it may be displayed in pr ...
" Chernoff faces; 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. 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 twin
Twins are two offspring produced by the same pregnancy.MedicineNet > Definition of TwinLast Editorial Review: 19 June 2000 Twins can be either ''monozygotic'' ('identical'), meaning that they develop from one zygote, which splits and forms two ...
s, for example, and are useful in grouping as pairs of Chernoff faces would be.
Chernoff fish
In ''Visualizing Financial Data'' (2016, ), Julie Rodriguez and Piotr Kaczmarek use "Chernoff fish", where various parts of a cartoon fish are used to encode different financial details.
In literature
In Peter Watts' novel
''Blindsight'' (2006), a
transhuman
Transhuman, or trans-human, is the concept of an intermediary form between human and posthuman. In other words, a transhuman is a being that resembles a human in most respects but who has powers and abilities beyond those of standard humans. The ...
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.
In the sci-fi short story "Degrees of Freedom" by
Karl Schroeder
Karl Schroeder () (born September 4, 1962) is a Canadian science fiction author and a professional futurist. His novels present far-future speculations on topics such as nanotechnology, terraforming, augmented reality, and interstellar travel, ...
, Chernoff faces make a prominent appearances as a future technology, supporting the communication of aggregate sentiment and perspective.
References
Other sources
*
*
Further reading
* "Facial Representation of Multivariate Data", David L. Huff, Vijay Mahajan and William C. Black. ''
Journal of Marketing
The ''Journal of Marketing'' is a bimonthly scholarly journal that publishes peer-reviewed research in marketing. It is published by the American Marketing Association. Established in 1936, It is the fourth-oldest major journal covering marketing ...
'', Vol. 45, No. 4 (Autumn, 1981), pp. 53–59.Published by:
American Marketing Association
The American Marketing Association (AMA) is a professional association for marketing professionals with 30,000 members as of 2012. It has 76 professional chapters and 250 collegiate chapters across the United States.
The AMA was formed in from th ...
"FACES-A FORTRAN Program for Generating Chernoff-Type Faces on a Line Printer" Danny W. Turner and F. Eugene Tidmore. ''
The American Statistician
''The American Statistician'' is a quarterly peer-reviewed scientific journal covering statistics published by Taylor & Francis on behalf of the American Statistical Association. It was established in 1947. The editor-in-chief is Daniel R. Jeske, ...
'', Vol. 34, No. 3 (Aug., 1980), p. 187 Published by: American Statistical Association
"Representing Points in Many Dimensions by Trees and Castles"{Dead link, date=September 2018 , bot=InternetArchiveBot , fix-attempted=yes , B. Kleiner and J. A. Hartigan. ''
Journal of the American Statistical Association
The ''Journal of the American Statistical Association (JASA)'' is the primary journal published by the American Statistical Association, the main professional body for statisticians in the United States. It is published four times a year in Ma ...
'', Vol. 76, No. 374 (Jun., 1981), pp. 260–269. Published by the ''
American Statistical Association
The American Statistical Association (ASA) is the main professional organization for statisticians and related professionals in the United States. It was founded in Boston, Massachusetts on November 27, 1839, and is the second oldest continuous ...
''
*Gonick, L. and Smith, W. ''The Cartoon Guide to Statistics''. New York: Harper Perennial, p. 212, 1993.
* Moriarity, S. (1979). "Communicating financial information through multidimensional graphics". Journal of Accounting Research 17, 205-224.
* Stock, D. and Watson, C. (1984). "Human judgment accuracy, multidimensional graphics, and humans versus models". ''
Journal of Accounting Research
The ''Journal of Accounting Research'' is a leading peer-reviewed academic journal associated with the University of Chicago. It was established in 1963 and is published by Wiley-Blackwell on behalf of the Accounting Research Center (Formerly the I ...
'' 22, 192-206.
*''Information Visualization: Perception for Design'' (2004), Ware C.
"The Empathic Visualisation Algorithm: Chernoff Faces Revisited"(21
"An empirical evaluation of Chernoff faces, star glyphs, and spatial visualizations for binary data" Michael D. Lee, Rachel E. Reilly, Marcus E. Butavicius. ACM International Conference Proceeding Series; Vol. 142, Proceedings of the Asia-Pacific symposium on Information visualisation - Volume 24
Raciborski 2009, ''The Stata Journal'' 9, Number 3, pp. 374–387
External links
-(''
The New York Times
''The New York Times'' (''the Times'', ''NYT'', or the Gray Lady) is a daily newspaper based in New York City with a worldwide readership reported in 2020 to comprise a declining 840,000 paid print subscribers, and a growing 6 million paid ...
''; Chernoff faces generated from manager performance data)
"A Critique of Chernoff Faces"- Robert Kosara, published February 25, 2007
Java visualizationExample and codefor the
R statistical software environmentExample and codefor
Python using the
matplotlib
Matplotlib is a plotting library for the Python programming language and its numerical mathematics extension NumPy. It provides an object-oriented API for embedding plots into applications using general-purpose GUI toolkits like Tkinter, wx ...
library
ChernoffFace packagein
Python using the
matplotlib
Matplotlib is a plotting library for the Python programming language and its numerical mathematics extension NumPy. It provides an object-oriented API for embedding plots into applications using general-purpose GUI toolkits like Tkinter, wx ...
library
Function ChernoffFacein
Wolfram Language
The Wolfram Language ( ) is a general multi-paradigm programming language developed by Wolfram Research. It emphasizes symbolic computation, functional programming, and rule-based programming and can employ arbitrary structures and data. It is ...
(
Mathematica
Wolfram Mathematica is a software system with built-in libraries for several areas of technical computing that allow machine learning, statistics, symbolic computation, data manipulation, network analysis, time series analysis, NLP, optimi ...
) a
Wolfram Function Repositoryfor
MATLAB
MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementa ...
usin
Statistics and Machine Learning Toolbox
"Mapping Quality of Life with Chernoff Faces", Joseph G. Spinelli and Yu Zhou"SUGI 26: Escaping Flatland: Chernoff's Faces Revisited"-(modifying FACES for more aesthetic output)
-(a
Mac OS X
macOS (; previously OS X and originally Mac OS X) is a Unix operating system developed and marketed by Apple Inc. since 2001. It is the primary operating system for Apple's Mac computers. Within the market of desktop and lapt ...
screensaver which generates random Chernoff faces)
NovoSpark Visualizer- an advanced visualization tool that enables qualitative analysis of multidimensional data through the exploration of a graphical image.
"How to visualize data with cartoonish faces ala Chernoff" (Flowing Data)Baseball faces- at the Institute for Quantitative Social Science at Harvard University
Statistical charts and diagrams