0
$\begingroup$

When I normalize a data set and compute the cosine similarity between the rows, the cosine similarity differs from the one without any normalization.

Say there are 4 2D vectors: (1, 1), (2, 2), (1, 2) and (2, 1) Before normalization: cosineSimilarity between (1,1) and (2,2) is 1.0

After normalization these vectors become: (-0.5, -0.5) and (0.5, 0.5) The cosine similarity becomes -1.0

The interpretation changed completely.

Does this mean that when using KNN, Kmeans or any distance based algorithm on a dataset that uses the cosine similarity, normalization should be avoided?

$\endgroup$
  • 1
    $\begingroup$ Your sense of "normalize" appears to include recentering. Because that shifts these vectors, then of course the angles change. Please see stats.stackexchange.com/questions/22329. $\endgroup$ – whuber Mar 29 '17 at 17:23
  • $\begingroup$ Are you explictly talking about normalization or do you mean scaling? $\endgroup$ – Unhandled exception Mar 29 '17 at 23:23
  • $\begingroup$ Doesn't normalization include a recentering by mean subtraction? The scaling would be invariant to the cosine similarity I believe. $\endgroup$ – AbhinavChoudhury Mar 31 '17 at 3:03

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.