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?