title: Strange behaviors when implementing matrix factorization in Keras
body: <p>I'm implementing a simple model of matrix factorization for recommendation using Keras. I found some strange behaviors when running the model:</p>
  
  <ul>
  <li>The users' and items' latent factors tend to go to zero vector.</li>
  <li>Even I only try to fit nonzero values (which have value of 1), those latent factors still go to 0. More strangely that the training and validation losses are decreased even the difference between true values (which are always 1) and predicted values (which are the dot products between users' and items' latent factors) should be increased (because those latent factors are becoming zero). I use 'mse' as the loss metric.</li>
  </ul>
  
  <p>I don't know what happened. If anyone has encountered this issue before, I'll be appreciated if you can share your solution. (Sorry that I cannot post my code, because it is quite messy). Thank you.</p>