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I need to find how well several different lists match a reference list. I'm looking for a percentage or some kind of similarity score.

For example, 

a = {"A278", "G279", "S280", "G281", "I282", "I283", "I284", "S285", 
"D286", "T287", "P288", "V289", "H290", "D291", "C292"}
b = {"S280", "G281", "I282", "I284"}
c = {"C275", "S276", "T277", "A278", "G279"}

How can I determine that b is a better match against a than c? a is the reference list.

Order matters.

After looking through the documentation, the only way I can think of doing this is to iterate through b and c and test if each element is MemberQ of a, tallying up the total and comparing the totals at the end. Is there a better approach?

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    $\begingroup$ You might consider looking through the whole bunch of *Distance[]/*Dissimilarity[] functions available. SequenceAlignment[] might also be of use. $\endgroup$
    – J. M.'s missing motivation ♦
    Commented Oct 8, 2018 at 4:24
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    $\begingroup$ Testing as described in the last paragraph of the question does not take account of order. If order actually does not matter, consider Complement. $\endgroup$
    – bbgodfrey
    Commented Oct 8, 2018 at 4:33
  • $\begingroup$ Working on Complement now, it seems promising @bbgodfrey $\endgroup$
    – brienna
    Commented Oct 8, 2018 at 4:37

7 Answers 7

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Maybe:

LongestCommonSequence[a, b]

{"S280", "G281", "I282", "I284"}

LongestCommonSequence[a, c]

{"A278", "G279"}

Length@LongestCommonSequence[a, #] & /@ {b, c}

{4, 2}

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MaximalBy[Length[a⋂#]&]@{b,c}

{{"S280", "G281", "I282", "I284"}} 

MinimalBy[Length@Complement[a,#]&]@{b,c}

{{"S280", "G281", "I282", "I284"}}

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  • $\begingroup$ +1 for conciseness, this is better than my answer $\endgroup$
    – brienna
    Commented Oct 8, 2018 at 5:21
  • $\begingroup$ @briennakh, yours is probably faster. $\endgroup$
    – kglr
    Commented Oct 8, 2018 at 5:22
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Suppose I have the reference list a and a matrix otherLists of all other lists I want to compare against a:

otherLists[[Ordering[Length[#] & /@ (Complement[a, #] & /@ otherLists), 1]]]

This will return the list that best matches a.

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    $\begingroup$ you can use just Length instead of Length[#] &. $\endgroup$
    – kglr
    Commented Oct 8, 2018 at 5:28
  • $\begingroup$ Please don't edit my answer @MarcoB — Write a comment. $\endgroup$
    – brienna
    Commented Feb 20, 2019 at 18:18
  • $\begingroup$ I rolled back my changes. @kglr 's comment is suggesting the same change. Is there a reason you prefer to retain your version? $\endgroup$
    – MarcoB
    Commented Feb 20, 2019 at 18:21
  • $\begingroup$ My answer works. If you want to optimize my answer, you can add your suggestion as a comment or upvote kglr's comment. Thank you. @MarcoB $\endgroup$
    – brienna
    Commented Feb 20, 2019 at 18:23
  • $\begingroup$ @briennakh It certainly works, but the usage of Length[#]& where Length would suffice is unnecessary. This site is collaboratively edited, so I made a change that, in my opinion, improved this answer for future readers. Anyway, I will leave it as it was; perhaps you might consider making a change yourself. $\endgroup$
    – MarcoB
    Commented Feb 20, 2019 at 18:33
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Going off your percent similarity idea, maybe something like

listsim[ref_, test_] := {#, 100. (1 - Length@Complement[ref, #]/Length@ref)} & /@ test

listsim[a, {a, b, c}]

{{{A278,G279,S280,G281,I282,I283,I284,S285,D286,T287,P288,V289,H290,D291,C292},100.} {{S280,G281,I282,I284},26.6667}
{{C275,S276,T277,A278,G279},13.3333}}

which ended up being in a similar vein to your answer.

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  • $\begingroup$ I like this!! Thanks! $\endgroup$
    – brienna
    Commented Oct 8, 2018 at 5:18
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Using SequenceAlignment:

a = {"A278", "G279", "S280", "G281", "I282", "I283", "I284", "S285", 
  "D286", "T287", "P288", "V289", "H290", "D291", "C292"};
b = {"S280", "G281", "I282", "I284"};
c = {"C275", "S276", "T277", "A278", "G279"};

SequenceAlignment[a, b] // Select[VectorQ] // MaximalBy[Length]

{{"S280", "G281", "I282"}}

SequenceAlignment[a, c] // Select[VectorQ] // MaximalBy[Length]

{{"A278", "G279"}}

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a = {"A278", "G279", "S280", "G281", "I282", "I283", "I284", "S285", 
     "D286", "T287", "P288", "V289", "H290", "D291", "C292"};

b = {"S280", "G281", "I282", "I284"};

c = {"C275", "S276", "T277", "A278", "G279"};

Using DeleteCases:

DeleteCases[a, Except[Alternatives @@ b]]

{"S280", "G281", "I282", "I284"}

DeleteCases[a, Except[Alternatives @@ c]]

{"A278", "G279"}

Length@DeleteCases[a, Except[Alternatives @@ #]] & /@ {b, c}

{4, 2}

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$\begingroup$ 
a = {"A278", "G279", "S280", "G281", "I282", "I283", "I284", "S285", 
   "D286", "T287", "P288", "V289", "H290", "D291", "C292"};

b = {"S280", "G281", "I282", "I284"};

c = {"C275", "S276", "T277", "A278", "G279"};

Using SymmetricDifference (new in 13.1) and TakeSmallestBy (new in 10.1)

Extract[{b, c},
 TakeSmallestBy[
  Map[SymmetricDifference[a, #] &, {b, c}] -> {"Index"},
  Length,
  1]]

{{"S280", "G281", "I282", "I284"}}

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