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I know that as a question it may seem stupid, but in case it is applying K NN with k = 1 and I have two neighbors at the same distance , what is the best approach to carry out the classification ?

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The best approach would really depend on your application and what is important too you.

However, things you can try include:

  • Increase K until there is no tie anymore - if you increase to 2, you will likely have another tie, since they are at the same distance already. So, 3 or higher should do the trick.
  • Include another feature to your classifier - adding another dimension to your space could solve the problem if the values for both these data points are different.
  • Choose another distance metric - you could have a preferred way of measuring distance, but for ties, chose another metric that will break it.
  • Establish a rule for breaking ties, e.g.
    • Pick the class with the most observed data points
    • Randomly assign a class

More information on your application would help to choose a best approach.

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