The graphical representation of two dimensional variables is rather straightforward. Three dimensional variables presents more of a challenge, but dealing with higher dimensions is much more difficult. Two methods using profiles and stars suffers from a confusion of which variable is represented when the dimensionality is greater than six.
The method called “Chernoff Faces” (Chernoff 1973) involves a computer program which draws a caricature of a face when given 18 numbers between 0 and 1. These numbers correspond to features of the face. Thus one may represent the length of the nose, another curvature of the mouth, and a third the size of the eyes. If we have 12 dimensional data, we can adjoin 6 constants to get points in 18 dimensional space, each represented by a face. As the point moves in 18 dimensional space the face changes.
The method was developed in response to a problem in cluster analysis (see Cluster Analysis: An Introduction). There are many methods proposed to do...
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Chernoff H (1973) The use of faces to represent points in k-dimensional space graphically. J Am Stat Assoc 68:301–308
Chernoff H, Rizvi MH (1975) Effect on classification error of random permutations of features in representing multivariate data by faces. J Am Stat Assoc 70:548–554
Jacob RJK (1978) Facial representation of multivariate data. In: Wang PCC (ed) Graphical representation of multivariate data. Academic, New York, pp 143–168
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Chernoff, H. (2011). Chernoff Faces. In: Lovric, M. (eds) International Encyclopedia of Statistical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04898-2_171
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