The Use of Faces to Represent Points in k-Dimensional Space Graphically

This is my new favorite thing.

Herman Chernoff’s 1972 paper, “The Use of Faces to Represent Points in k-Dimensional Space Graphically.” The name is pretty self-explanatory: it’s an attempt to represent high dimensional data…through the use, as Chernoff explains, of “a cartoon of a face whose features, such as length of nose and curvature of mouth, correspond to components of the point.”

Here’s an example:

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I just find this hilarious.

But, as crazy as this approach may seem – there’s something really interesting about it. Most standard efforts to represent high dimensional data revolve around projecting that data into lower dimensional (eg, 2 dimensional) space. This allows the data to be shown on standard plots, but risks loosing something valuable in the data compression.

Showing k-dimsional data as cartoon faces is probably not the best solution, but I appreciate the motivation behind it – the questioning, ‘how can we present high dimensional data high dimensionally?’

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