Cliff Pickover's Face Generation for Data Analysis and Educational Assessment

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"The most exotic journey would not be to see a thousand different places, but to see a single place through a thousand person's eyes."
Presented on this page is a rather unorthodox computer graphics characterization of data that I have used in applications ranging from sounds to DNA sequences. Please forgive me if the page is sluggish -- it's doing a massive amount of real-time computation on your machine!

In particular, you can use a computer-controlled face to represent data. These cartoon faces can be used to represent the values of as many as 10 variables, each variable corresponding to a facial feature. You can read all about the method and my applications in my book Computers, Pattern, Chaos and Beauty. (For example, I've used the faces to examine cancer gene sequences, for presenting sounds to deaf children, etc.)

As background, computer graphics has become increasingly useful in the representation and interpretation of multidimensional data with complex relationships. Pseudo-color, animation, three-dimensional figures, and a variety of shading schemes are among the techniques used to reveal relationships not easily visible from simple correlations based on two-dimensional linear theories.

Showing correlations between two or three variables is easy: simply plot a two-dimensional or three-dimensional graph. But what if one is trying to present four or five or even ten different variables at once? The face method of representing multivariate data was first presented in 1973 by Chernoff, a Harvard statistician. Using gradations of various facial features, such as the degree of eyebrow slant or pupil size, a single face can convey the value of many different variables at the same time. Such faces have been shown to be more reliable and more memorable than other tested icons (or symbols), and allow the human analyst to grasp many of the essential regularities and irregularities in the data. In general, n data parameters are mapped into a figure with n features, each feature varying in size or shape according to the point's coordinate in that dimension. The data sample variables are mapped to facial characteristics; thus, each multivariate observation is visualized as a computer-drawn face. This aspect of the graphical point displays capitalizes on the feature integration abilities of the human visual system and is particularly useful for higher levels of cognitive processing. The drawing on this page shows the range of faces produced when random numbers ("white noise") are mapped. This shows you the diversity of computer-generated faces. The settings for each of the ten facial parameters were computed using a random number generator. (Code for creating the faces is given in the book. This Java applet for displaying the faces on this page was written by the wonderful AI programmer John Wiseman.)

In my applications ten facial parameters, F(1, 2, 3, 4, 5, 6, 7, 8, 9, 10) are used, and each facial characteristic has ten settings, S(1, 2, 3, 4, 5, 6, 7, 8, 9, 10), providing for 10 billion possible different faces. The controlled features are: head eccentricity, eye eccentricity, pupil size, eyebrow slant, nose size, mouth shape, eye spacing, eye size, mouth length, and degree of mouth opening. Head eccentricity, for example, controls how elongated the head is in either the horizontal or vertical direction. The mouth is constructed using parabolic interpolation routines, and the other features are derived from circles, lines, and ellipses.

In my studies, faces computed from speech sounds (i.e. "speech-faces") could provide useful biofeedback targets for helping deaf and severely hearing-impaired individuals to modify their vocalizations in selective ways -- especially since they may provide simple and memorable features to which children could relate. The traditional speech spectrogram displays are not the same as pictures, since pictures have numerous visual features that can be readily identified, labeled, and integrated into a coherent whole. To compare SDPs (previous section) and faces: note that unlike faces, SDPs do not elicit an emotional reaction. Emotion does confer a mnemonic advantage for the faces, but can sometimes obscure the association, e.g. a smiling face representing cancer statistics.


A number of recreational and educational uses for the faces are suggested in the following sections. As background, research has demonstrated the potential value that visualization and iconic systems play in learning and instruction. Popular educational software for home computers is becoming available (e.g., the "FaceMaker" by Spinnaker (see references)) which allows children to create faces from sets of eyes, ears, and noses. Programs such as these help children become comfortable with computer fundamentals such as menus and cursors. The computer-drawn faces presented in the current section have particular value in that they are created under parametric control and can provide immediate visual feedback to the user. In addition, any face can easily be regenerated at a later time from its control-data.

Cognitive Association of Coordinates with Facial Features

There have been several studies in the literature which have explored the child'ss ability to organize and represent body location information. Here, a simple face-drawing system was developed where children can type numbers at the terminal keyboard and immediately view the results on an adjacent graphics screen. For example, faces were constructed from the control-data entered by Lisa, a 6-year-old girl with no prior experience with computers. One face in particular was her favorite, because she found the shape of the mouth amusing. She worked on the figure for several minutes, developing the mouth to her specifications, and subsequently she recorded the final control-data on a piece of paper. This indicated that she understood the concept of number-to-face parameter mapping.

Target-Pictures for Children

In my book, drawings made by children in an attempt to reproduce the four computer-drawn targets at top. From top to bottom, the ages of the children were 6 , 6, 8, and 10. The faces can be used to illustrate the concept of similarity, sameness, and difference. Since the facial parameters are accurately controlled, the degree of difficulty of the task can be specified. The faces may also serve as target-pictures for children to draw. Because the computer faces are created from control-data, the resultant faces can easily be regenerated at a later time, or altered slightly, in order to test hand-eye coordination and development. includes four computer-drawn faces and children's attempts to reproduce them. The drawing task can be made much more difficult if the child is asked to view the face first and then required to draw it as well as possible from memory. Computer software, and hardware such as digitization tablets, make an analytic comparison between computer- and child-generated faces easy. Simple parameters such as center of gravity, and radius of gyration can be computed to characterize the drawings in an objective way.

For years psychologists have tried to determine when infants first realize how the features of the human face are naturally arranged and when an infant's ability to perceive facial expressions begins. Computer-generated faces might be ideal for the study of infant's perception of natural and distorted arrangements of a schematic face. In the study of Maurer and Barrera (1981), it was shown that 2-month-old infants show a preference for a natural arrangement of facial features on a cartoon face, as opposed to scrambled features. Though their cartoon faces were not computer-generated, computers could be used in the placement (random or otherwise) of the facial features on the head, giving the researcher rigorous control of the resultant expressions.

Learning by Means of Analogy

The faces can be used to illustrate the concept of similarity, sameness, and difference. Since the facial parameters are accurately controlled, the degree of difficulty of the task can be specified. Possible tasks include: Which two are the same? and Which one is different? The faces can be used to explore memory abilities: initially, one face is shown, then erased, and the user can subsequently be asked to choose the face from a small group, somewhat like picking from a police line-up.

Educational Aid for the Presentation of Statistical Concepts

The faces may be suitable as visual supplements in the presentation of statistical concepts, particularly distribution theory, to individuals inexperienced in mathematics and with no prior knowledge of the methods of statistical evaluation. In this work, faces were used to illustrate the concept of white noise (totally random distribution) such as that shown on this page in contrast to Gaussian noise (normal error distribution), theories usually not introduced to individuals prior to the high-school level due to the mathematical complexity of the subject matter. For the case of white noise, one hundred faces were generated, each facial characteristic having a setting determined from a random number generator. For very young students, the faces could be used, in addition to standard techniques, for visualizing simpler concepts such as the mean, median, mode, and other measures of central tendency.

Commercial and Military Air Traffic Control

One may speculate about potentially useful applications of the computer-drawn faces in the cockpit of airplanes. The growing complexity of aircraft controls and readouts are making aircraft almost too complex to fly. The faces can accommodate analog or digital input from a multitude of readouts, each facial parameter receiving input from one or more gauges. Deviations in the controls from their expected values would give rise to excursions of the facial parameters from their middle settings. While it is true that the more standard concept of having a gauge blink or beep when a parameter has gone beyond a critical value is valuable, the faces would be especially useful in alerting the pilot of conditions where several readings are not themselves at critical stages, but where the combined effect may be dangerous.

Other faces links: here, here, here. Faces for pain representation: here.

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