# CHERNOFF FACES IN R

Chernoff faces is a technique from multivariate analysis. The Chernoff faces technique was developed by Herman Chernoff and was presented in a paper in 1973 in the Journal of the American Statistical Association. Chernoff faces provide an intuitive way of looking at variation within a data set where the data is in a matrix of rows and columns (for example, a two way contingency tables).  A different face is created from each row in the data set. The differences between the faces are based on the columns of the data set. Each column is associated with one part of a facial expression (the first column is associated with the height of the face, the second with the width of the face, etc.). Chernoff designed the method for up to 18 facial components.  The faces() function in the TeachingDemos package of R uses 15 facial components, which were used here.

### Components of the Faces

From  help page for the function faces(), the fifteen components in R are the height of the face, width of the face, shape of the face, height of the mouth, width of the mouth, curve of the smile, height of the eyes, width of the eyes, height of the hair, width of the hair, styling of the hair, height of the nose, width of the nose, width of the ears, and height of the ears.  If the number of columns in the matrix is less than 15, the function will cycle back through columns until 15 columns are used.  One way around the problem is to put a constant value in the excess columns.  In what is presented here, cycling was done.

### Description of the Data

The Chernoff faces below were generated using the function faces() in the TeachingDemos package of R and are plots of the differences between facial expressions in the The Astrofaces Data Set. The Astrofaces Data Set was created from the pictures at the website, http://www.astrofaces.com, where an astrological group has gathered photographs from over 4700 persons, along with the placement of the Sun, Moon, and Ascendant for each person. In the spring of 2002, I went though the photographs and classed the faces as to whether the face had an open smile, a closed smile, an open mouthed neutral expression, a closed mouth neutral expression, an open frown, or a closed frown. For each person, I recorded the expression and the elements of the Sun, Moon, and Ascendant (the elements in astrology are air, earth, fire, and water). There were 2015 photographs in the data set at the time.

I have used a variety of techniques over the years to try to find a relationship between the elements of the Sun, Moon, and Ascendant and the expressions in the photographs, with little to show for my effort. So far, correspondence analysis has given the best results. (That said, I encourage anyone who thinks that there is nothing to astrology to visit the Astrofaces website and look at groups of photos.)  Few persons had open frowns.  The expressions on the persons at the Astrofaces website are not to be confused with the facial expressions of the Chernoff faces.

The input file for the faces() function in R was a table of normalized counts with astrological elements in the rows and facial expressions in the columns. In the four rows were counts of the number within the element with each of the six facial expressions divided by the total number of persons in the element. The plots are for the Sun, Moon, and Ascendant data, each done separately. In the post for astrological researchers posted earlier on this site, there is a plot of the combined data.

### The Sun Faces

The first column – open smiles – controls height of face, height of eyes and width of nose; the second – closed smiles – width of face, width of eyes and width of ears; the third – open neutrals – shape of face, height of hair, height of ears; the fourth – closed neutrals – height of mouth and width of hair; the fifth – open frowns – width of mouth and styling of hair; and the sixth – closed frown – curve of smile and height of nose.

In the Sun plot, we can see that the air and fire faces have similar sizes and shapes but different expressions, so air and fire are somewhat similar with regard to the first three columns (open smile, closed smile,  and open neutral), but not with regard to the last three columns (closed neutral, open frown, and closed frown).  Water and earth have the same shape- so are similar with respect to open neutrals, but are different sizes – so are different with respect to open and closed smiles.  Other than the open neutrals, the two elements are different.

The raw table of counts for the Sun data is given below.  The zero under open frowns for the water element causes a degeneracy in the water face.

 Open Smile Closed Smile Open Neutral Closed Neutral Open Frown Closed Frown Air 104 31 32 100 3 26 Earth 97 35 40 104 1 28 Fire 108 32 31 101 2 29 Water 107 41 36 93 0 34

### The Moon and Ascendant Faces

The Chernoff faces for the Moon and Ascendant are plotted below.

In the Moon and Ascendant plots, we can follow the same procedure as with the Sun to evaluate the expressions.

### Conclusions

We can see from the plots for the Sun, Moon, and Ascendant that the faces tell us something intuitive about the differences between the four astrological elements with regard to the six facial expression classes in the Astrofaces dataset. Looking between plots, we can also see similarities across the Sun, Moon, and Ascendant for differing elements.