math - Similarity measure of vectors -


i want discuss similarity measure meets requirements. vectors that:

a = (-4,0,4,null) b = (-2,null,-4,null) c = (4,4,4,4) d = (0,0,0,0) e = (null,null,null,null) f = (-4,-4,-4,-4)

the values activity values in range -5 +5. value of 0 stand non active value , values near -5 , +5 stand high active value. searching right similarity measure.

i want similarity between combinations of these vectors. think similarity between c , f must 1 , similarity between c , d must 0:

c:e = 0 c:f = 1 c:d = 0 a:b = think on 0.5

i hope unterstand requirements. question now: similarity measure meet requirements?

edit:

  • 0 not same null. null not defined
  • the similarity measure needs calculate similarity between 2 vectors

this complicated, first of c , f similar want start taking absolute value. similarly, looks null should translated 0.

this result in vectors elements in range 0..5, simplifies problem bit.

then question how want it, starting taking component wise difference start, question how weight them together, random guess either linear combination or maybe quadratic.

really, depends on use-case useful on last step, think if can start getting elements 0..5 range lot gained.


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