The two layers of data used here.

<p>At the top, we see a sample of four colors, as well as the CIE L*a*b* distances between all pairs among these colors. Below, we see a hypothetical sequence of color naming responses. Various papers by Kay and coauthors <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0089184#pone.0089184-Kay1" target="_blank">[2]</a>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0089184#pone.0089184-Kay2" target="_blank">[8]</a>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0089184#pone.0089184-Kay3" target="_blank">[17]</a> pick out a best representative point in the space above and replace any distribution below with this single representative. Lindsey & Brown <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0089184#pone.0089184-Lindsey1" target="_blank">[4]</a> point out that this approach, by ignoring most of the structural information contained in the concrete distributions in the data below loses significant information about color naming systems and patterns. Lindsey & Brown and Jäger <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0089184#pone.0089184-Jger1" target="_blank">[9]</a> on their hand focus on the distributions of responses in the lower part of this figure, ignoring completely the perceptual distances in the color space above. In this paper, we argue that a better way is to work with methods that include both layers of the data: that work both with the perceptual distances above and the distributions below.</p>