My Data Have Feelings

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:
 

chernoff_1

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:

Characteristic Metric
Face size Spend
Hair length Number of clicks
Face shape CTR
Smile CPA (spend/leads)
Conversion rate Size of eyes
Avg. position Size of nose
CPC Ear size

 
And the results ? Drum roll please……

chernoff

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.

Related Topics: Channel: Analytics | Search & Analytics

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About The Author: is Director, Business Analytics at Adobe. He leads a global team that manages the performance of over $2 BN dollars of ad spend on search, social and display media at Adobe.

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  • http://searchmarketingcommunications.com Tim Cohn

    Pretty cool…

    Haven’t you shown us the data in seven dimensions?

  • http://www.efrontier.com sidshah

    You are right. I have shown data in 7 dimensions. 6 is a typo. Hmm… now we could add a moustache as an 8th. Fu Manchu’s here we come !!

  • http://www.chadsummerhill.com ChadSummerhill

    Very interesting, Siddharth! Your article got me thinking about how cool it would be if Tableau added Chernoff faces to their visualization software. I even added a post to my blog in honor of your article.

    http://www.chadsummerhill.com/siddharth-chernoff-faces/

  • http://www.efrontier.com sidshah

    Hi Chad,
    Glad you like it. I did the visualization in R. It has a built in library that can do chernoff faces. If you know R its quite straight forward !

    If you speak to hard core data/stats guys they would not like chernoff faces as it has such a qualitative feel. Then again, they are not marketers !

    Sid

  • http://www.chadsummerhill.com ChadSummerhill

    Hi Sid,

    I wonder how hard it would be to add Size and Color to the R library. A little color could help a lot with this type of visual.

    Ever used Tableau? Written any articles about it?

    Thanks,
    Chad

  • http://www.fingo.co.uk BenMorel

    Wouldn’t this data be more useful in correlation graphs? I have a feeling that othes would be more receptive to it that way.

    Pulling together a quick scatter graph in Excel would instantly show you that ad position and CPA, your chosen reference metric, were not correlated – this column could then be removed from the study as it is not an influencing factor. CPA and conversion rate you would expect to be well correlated and again a quick scatter graph would probably show you that they are – proving quantitatively that your first bullet under “what do these faces tell us?” is correct.

    The biggest things I imagine that Management, or pretty much anyone, would respond to would be correlations of “Visits vs CPC” and “Visits vs conversion rate” – especially if there were any anomolies. The anomoly of Boston’s low conversion rate, for example, would be immediately obvious and all of this data would be actionable.

    How would you action the data presented by the faces? Unfortunately I fail to see the time or visualisation advantage the Chernoff faces bring.

  • http://www.efrontier.com sidshah

    Hi Ben,

    Like I said before quants dont like Chernoff faces . In fact you can find numerous critiques on it. However, I can see instances where they would be very useful

    You can create a correlation matrix with the above data but my personal experience showing to data with non-quant management people is that it can often overwhelm them. This is specially true when you have more than 4 -5 metrics. Also, when you have so many metrics a 2 dimensional correlation often doesn’t tell the story… but thats a different blog post all together :)

    Chernoff faces work well with people who are not oriented to think quantitatively and also when you want to mix disparate data into one qualitative metric. So lets say you want to assess the quality of management of a google campaign. The factors could be

    a. Avg Quality score
    b. Avg CTR
    c. Avg. number of ad variations
    d. Volume
    e. Ratio of keywords to ad groups
    f. Total keywords

    These are disparate metrics and it is hard to get a qualitative feel for a campaign’s “management quality”. I can see chernoff faces being useful here.

    Here is another example that shows chernoff faces for Quality of life

    http://proceedings.esri.com/library/userconf/educ04/papers/pap5000.pdf

    Chad: The above link also shows how you can use colors with chernoff faces effectively.

 

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