Venn and Euler Data Diagrams

Scientists conducting microarray and other experiments use Venn and Euler diagrams to analyze and illustrate their results. Most existing computer programs that implement Venn and Euler diagrams are limited to three sets. The few programs that plot more than three sets rest on ad-hoc methods, such as force-directed algorithms designed for laying out graphs. As a general solution to this problem, this article introduces a statistical model for fitting Venn and Euler diagrams to observed data. The statistical model outlined in this report includes an explicit loss function and a minimization procedure that enables formal estimation of the Venn/Euler model for the first time. A significance test of the null hypothesis is computed for the solution. Residuals from the model are available for inspection. As a result, this algorithm can be used for both exploration and inference on real datasets. A Java program implementing this algorithm is available under the Mozilla Public License. An R function venneuler() is available as a package in CRAN.