As search marketers, we are often asked to look at multi-dimensional data. This is often cumbersome, boring and overwhelming to go through. Take a look at this example from a campaign that’s running in multiple cities in the US:
 

The CPA in Boston is high and it appears to be due to the conversion rate. However, a quick glance at this data surfaces several questions: how much better or worse is this performance with respect to the others? How are the high volume campaigns doing with respect to the lower volume ones? Does CPC have any connection with performance? I could answer all these questions by crunching the numbers and making additional tables but is there a quicker way to get a qualitative assessment of the data?

Yes—Chernoff faces. Herman Chernoff, a statistician, introduced “Chernoff faces” in a 1973 paper where he used simple cartoon faces to display complex multivariate data. Chernoff faces take advantage the human brain’s innate ability to simultaneously recognize small differences in many facial characteristics to come up with a general assessment of an emotion or a mood. In his paper, Chernoff encoded each of several variables to a facial characteristic such as the nose, eyes, lips, smile and so on to generate faces that represented data points. Let’s try his idea for the data above. I have encoded the metrics with the following features:

 
And the results ? Drum roll please……

What do the faces tell us?

• Ft. Lauderdale, Tampa, Cincinatti, Nashville, Raleigh-Durham, Atlanta and Charlotte have happy faces as their CPAs are lower than average. In fact, Atlanta (which has the lowest CPA) has a smile only seen in BFFs! All these campaigns have larger eyes indicating that they enjoy higher conversion rates.
• The unhappy faces are Boston, Philadelphia and Minneapolis. Here the eyes are small indicating that conversion rates are low. Note that ear sizes are very similar indicating that CPC is not to blame for the poor CPAs.
• Nose sizes are all over the place. This tells us that average position is not connected to overall performance here.
• DC, Tucson and Baltimore are the larger faces indicating that they are high volume campaigns. The campaigns are spend-ordered and hence as we go down the list the faces get smaller and smaller.

The pros and cons of Chernoff faces

Chernoff faces can be a quick way to qualitatively assess the performance of a campaign. Even if I had not shown you the data table, you would have intuitively guessed which campaigns were doing well and which were not based on the perceived “mood” of your campaigns. Note that even though I have shown you the performance of 25 campaigns in six dimensions, you were able to pick out the good and bad performers very quickly.

Chernoff faces can be used to represent multi-dimensional data in a very compact manner. While I represented six dimensions of data in the faces, my program lets me encode up to 15 dimensions such as length of lips, size of ears, the amount of hair and even the hair style!

One cannot make quantitative assessments with the faces. I can tell you Boston is doing poorly but I can’t tell you how much poorer than average. Hence, while I can make broad conclusions, I would need to dig into the data to tell you more.

Metric to facial feature mapping can alter your assessment. For this example, I had tried several different mappings to finally come up with the faces you see above. If I had mapped clicks to ear size, the faces would have looked quite different.

In all, Chernoff faces are an interesting way of visualizing multivariate data and can make mundane data analysis fun. And yes, afros rule!

For more information on Chernoff faces and to learn how to make your own faces, visit the Wikipedia Chernoff face page.

Opinions expressed in the article are those of the guest author and not necessarily Search Engine Land.

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