title: Proportional venn diagram for more than 3 sets
body: <p>I have a collection of documents in MongoDB where each has one or more categories in a list. Using map reduce, I can get the details of how many documents have each unique combination of categories:</p>
  
  <pre><code>['cat1']               = 523
  ['cat2']               = 231
  ['cat3']               = 102
  ['cat4']               = 72
  ['cat1','cat2']        = 710
  ['cat1','cat3']        = 891
  ['cat1','cat3','cat4'] = 621 ...
  </code></pre>
  
  <p>where the totals are for the number of documents that exact combination of categories.</p>
  
  <p>I'm looking for a sensible way to present this data, and I think a venn diagram with proportional areas would be a good idea. Using the above example, the area cat1 would be 523+710+891+621, the area of the overlap between cat1 and cat3 would be 891+621, the area of overlap between cat1, cat3, cat4 would be 621 etc.</p>
  
  <p>Does anyone have any tips for how I might go about implementing this? I'd preferably like to do it in Python (+Numpy/MatPlotLib) or MatLab.</p>