Suppose we have two vectors of same size but containing different values such as X=[1 2 3 4] & Y=[5 6 7 4].
How should we get the similarity score? Correlation coefficients or any better method is there to provide better results.
Dear Govind
correlations can be extracted by use the canonical correlations, it is suitable for finding relationship between vectors (sets of variables).
good luck
https://www.cs.cmu.edu/~tom/10701_sp11/slides/CCA_tutorial.pdf
http://www.google.com.sa/url?sa=t&rct=j&q=&esrc=s&frm=1&source=web&cd=7&cad=rja&uact=8&ved=0CF4QFjAG&url=http%3A%2F%2Fwww.unt.edu%2Frss%2Fclass%2Fmike%2F6810%2FCancorr.pdf&ei=tW1WVfjIB8z1UM_PgbgM&usg=AFQjCNFON2pLEc2-i3puhQFiTDh_C8UJeA
It all depends on what you mean by "similar": for example, if similar means close in Euclidean distance, just compute the length of |u-v|. On the other hand, if similar means "in similar directions", compute the angle between the vectors: (u.v)/( |u| |v|).
If similarity score means any sensible measure of the length of |x - y|, the vector norms relationship is provide the results.
Definition. Two norms ||⋅||α and ||⋅||β on a vector space X are called equivalent if there exist positive constants c1 and c2 such that
c1||x||β ≤ ||x||α ≤ c2||x||β, ∀x∈X.
For example, ∀x, y ∈ ℂn;
||x - y||∞ ≤ ||x - y||2 ≤ ||x - y||1 ≤ √n||x - y||2 ≤ n||x - y||∞.
To Sajeetha Thavareesan : See other 3 MOST POPULAR SIMILARITY MEASURES:
https://dataaspirant.com/2015/04/11/five-most-popular-similarity-measures-implementation-in-python/
There is a good comparison between famous similarity vector methods here,
https://www.analyticsvidhya.com/blog/2021/06/nlp-answer-retrieval-from-document-using-ts-ss-similarity-python/
https://github.com/taki0112/Vector_Similarity