title: How to validate Test set on trained SVD model?
body: <p>I'm following this tutorial on Matrix Factorization for Movie Recommendations in Python using <strong>Singular Value Decomposition (SVD)</strong>: 
   <a href="https://beckernick.github.io/matrix-factorization-recommender/" rel="nofollow noreferrer">here</a></p>
  
  <p>Using <strong>SVD</strong>, a dataset is approximated using SVD into three components:<br><br>
  <code>M ≈ U ⋅ S ⋅ Vt</code><br><br></p>
  
  <ul>
  <li>So you go from left (M) to the three components and back again,</li>
  <li>now you can use approx.</li>
  <li>M as a recommendation matrix.</li>
  </ul>
  
  <p>Now, i want to use train/test validation sets on this matrix, because you need to find the optimal k (number) approximation for M.</p>
  
  <p><strong>How does one apply a separate test set on a trained model to get the predictions for the unseen test set?</strong>
  What is the <strong>math / algorithm</strong> for this?
  Thanks</p>