title: DBSCAN clustering - what happens when border point of one cluster is considered to be core point of another cluster
body: <p>I would like to know your opinion about dbscan clustering, I am trying to implement algorithm as published <a href="https://www.aaai.org/Papers/KDD/1996/KDD96-037.pdf" rel="nofollow noreferrer">here</a>. In my opinion there is possibility for one point from border of some cluster to be an core point of another one as shown in picture:</p>
  <p><img src="https://i.stack.imgur.com/O2r3i.png" alt="" />.</p>
  <p>I think there are some of the possible solutions:</p>
  <ul>
  <li>we could consider point as written to cluster and that cannot be changed - but we could lost second cluster because of that</li>
  <li>we could be able to change border points cluster but without recomputing epsilon neighbourhood.</li>
  <li>we could be able to add point into multiple clusters (worst one).</li>
  </ul>
  <p>What do you think is the best? Or am I getting something completely wrong?</p>