Identical meaning, that it will produce identical results for a similarity ranking between a vector u and a set of vectors V.
I have a vector space model which has distance measure (euclidean distance, cosine similarity) and normalization technique (none, l1, l2) as parameters. From my understanding, the results from the settings [cosine, none] should be identical or at least really really similar to [euclidean, l2], but they aren't.
There actually is a good chance the system is still buggy -- or do I have something critical wrong about vectors?
edit: I forgot to mention that the vectors are based on word counts from documents in a corpus. Given a query document (which I also transform in a word count vector), I want to find the document from my corpus which is most similar to it.
Just calculating their euclidean distance is a straight forward measure, but in the kind of task I work at, the cosine similarity is often preferred as a similarity indicator, because vectors that only differ in length are still considered equal. The document with the smallest distance/cosine similarity is considered the most similar.