title: Should I return more suggestions then there are relevant documents in a precision-recall curve?
body: <p>I am trying to plot a precision-recall curve, but I have more document recommendations than relevant documents. Let´s say for one training example, there are just 3 relevant documents: A, C, E. But it could be all documents from A to Z. Then I vectorize this into:</p>
  
  <p>original = [1, 0, 1, 0, 1, ... ]</p>
  
  <p>And let´s say my prediction has the biggest values for A,C,E and small values for all other documents:</p>
  
  <p>prediction = [0.9, 0.1, 0.8, 0.1, 0.7, ... ]</p>
  
  <p>Then I calculate precision and recall for the top-k predictions, first only using the prediction with {0.9}, then with {0.9 , 0.8} and {0.9, 0.8, 0.7}. Until then my precision is 1. But after that, the precision can only drop because there are no more relevant documents. Is it right to go on calculating precision/recall with {0.9, 0.8, 0.7, 0.1,  ...}?</p>
  
  <p>I think I found the flaw by asking the question, when I return the recommendations {0.9, 0.8, 0.7} not only the precision is 1, but also the recall. I should stop to return documents then, right?</p>
  
  <p><strong>EDIT: The explanation is that more documents can be returned, but after returning all relevant docs the Recall stays 1, and the precision drops down in a straigt line.</strong></p>