CHERNOFF faces

In the CHERNOFF faces representation, eachparameter corresponds to one feature. Each face is one object. The CHERNOFF faces of the seven PAH in river sediments after feature standardization are demonstrated in Fig. 5-8. The information is the same as that represented in Fig. 5-7 by star plots but conclusions to be drawn are not so clear. 

Fig. 5-8. CHERNOFF faces of PAH in 45 selected river sediments from Thuringia, feature standardization. face width = naphthalene, ear level = fluoranthene, half-face height = benzo(b)fluor-anthene, eccentric upper face = benzo(k)fluoranthene, eccentric lower face = benzo(a)pyr-ene, nose length - benzo(ghi)perylene, mouth centering = indeno(l,2,3-cd)pyrene...

A selection of plotting and graphing techniques is shown in Table 8.1. Some graphing techniques that are mainly used in advertising and have not much scientific use are not mentioned, e.g. pie charts, 3D bar charts, Chernoff faces. On top of the graphical aspect, also greyvalues and colors can be used to represent aspects of data analysis. No color is used in this book. 

This style of representation is limited to three variables and even then the diagrams can become confusing, particularly for a lot of points. One method for graphically representing multivariate data ascribes each variable to some characteristic of a cartoon face. These Chernoff faces have been used extensively in the social sciences and adaptations have appeared in the analytical chemistry literature. Figure 1.13 illustrates the use of Chernoff faces to represent the data from Table 1.11. The size of the forehead is proportional to tin concentration, the lower face to zinc level, mouth to nickel, and nose to iron concentration. As with the three-dimensional scatter plot, two groups can... 

Figure 1.13 Data from Table I. II displayed as Chernoff faces...

All of the methods discussed so far for grouping of data cannot surpass the abilities of humans to recognize patterns. Therefore, more and more methods are developed that exploit the human ability for recognizing patterns. These graphical methods are based on a compact representation of multidimensionally characterized objects. We learn here about representation of multivariate data by star and sun-ray plots as well as by Chernoff faces. 

Figure 5.22 Graphical method for grouping of the hair data in Table 5.1 for representatives of the three subject groups a, b, and c (for assignments cf. Table 5.8). (A) Stars, (B) sun-rays, and (C) Chernoff faces.

Assignment of features to facial parts leads to representation of the objects as faces. Well known are the faces introduced by Chernoff. The features are characterized by facial parameters, such as the size or curvature of the eyes, the mouth, the eye brows, the nose, or the upper and lower half of the case. As an example, the hair data of the three subject types are plotted in Figure 5.22C, as Chernoff faces. 

Figure 5.23 Chernoff faces for distinguishing of serum samples of diseased and healthy patients on the basis of 20 clinical analyses.

One disadvantage of Chernoff faces is the fact that the individual faces cannot be varied independently of each other. Faces proposed by Flury-Riedwyl (cf. [1]) overcome this disadvantage. 

Chernoff Faces, Andrews Curves, Star Diagrams, and Parallel Coordinate Plots... 

Fig. 8.21. Starplots of five trace elements (directed as shown below) in 19 wine samples (a) CHERNOFF-type faces symbolizing five elements coded in the forms of the face, eyes, mouth, nose, and ears in four wine samples (b) (see Chernoff [1973]), and schematic representation of a tree plot of one sample characterized by 15 variables (c)...

Chernoff H (1973) The use of faces to represent points in k-dimensional space graphically. J Am Statist Assoc 68 361... 

CHERNOFF [1973] created an unusual graphical representation of multivariate data. Fie made the assumption that the human pattern recognition ability is best trained with human faces. Faces can be described with parameters like face width, ear level, half-face height, eccentric upper face, eccentric lower face, nose length, mouth centering, etc. 

Several other graphical techniques have been developed for a visual representation of multivariate data in two dimensions C3773. Chernoff C3733 described a curious method in which each pattern vector is represented by a cartoon face the features of the face are governed by the vector components. It is assumed that the human can easily recognize similar faces corresponding to a cluster of pattern points. 

---