title: Why is F1 measure effective for evaluating multiclass classifiers?
body: <p>I was looking for a good error metric for multiclass classifiers, and many people say that F1 measure is usually used.
  But given that predictions of multiclass classifiers are one-hot vectors, doesn't it mean there are no true positives when the prediction is wrong?
  What i mean is:</p>
  
  <p><a href="https://i.stack.imgur.com/IdFkM.png" rel="nofollow noreferrer">image</a></p>
  
  <p>when the prediction is correct, every element is true negatives except for the single '1'. So the precision here is just 1.</p>
  
  <p><a href="https://i.stack.imgur.com/3H0j1.png" rel="nofollow noreferrer">image</a></p>
  
  <p>And when the prediction is incorrect, there is no true positives. So the precision is 0.</p>
  
  <p>I would understand that F1 is a powerful metric method when it comes to multilabel classifications, since there can be more than one 1's in the vector, but applying F1 on multiclass classification seems a bit weird to me. Isn't it same with just accuracy?
  Or does it mean that F1 score <strong>per class</strong> should be used?</p>