IR Formulation.md

My idea for the score of an article would be as follows:

Sa = SUM( Ria * Rib * p * SCSi ) 

With Sa = Score of article Ria = Relevance of term i in article a Rib = Relevance of term i in article b p = Multiplier for term being in 'selected' paragraph SCSi = SCS score of term i with respect to selected term(s).

Some edge cases:

• SCSi = 1 for two selected terms
• SCSi = SCSi1 * SCSi2 * ... * SCSin for multiple selected terms.
• SCSi = (SCSi * 0.6) + 0.4 to not make it super-influential if no relations are found in 2 steps.

In SQL, this can be done in two ways:

• Create a FOR loop, looping over terms
• Cross-join the mediating relation table of Entities and Articles with itself and calculate.

Either can be done, the difference is probably in performance. It seems the loop would be a bit quicker, but I've no proof.

Method 1:

@ArtId = ID of article with requested text
@InParagraph = Array with entities in 'selected' paragraph
#SCS = Table with SCS scores of all non-selected entities

CREATE TABLE #tempCalc(
  id, ArtId, Score
)

INSERT INTO #tempCalc(id, ArtId, Score)
  (
   SELECT newid, C.ArtId, 0
   FROM Cross AS C
   WHERE C.TermId IN (
     SELECT C1.TermId 
     FROM Cross AS C1
     WHERE C1.ArtId = @ArtId
     )
  ) 

FOR t IN SELECT TermId 
	 FROM Cross
	 WHERE ArtId = @ArtId
LOOP

  UPDATE #tempCalc
  SET Score = 
   Score + 
     (SELECT C.Relevance
      FROM Cross AS C
      WHERE C.TermId = t
      AND   C.ArtId  = #tempCalc.ArtId
     ) *
     (SELECT SELECT C.Relevance
      FROM Cross AS C
      WHERE C.TermId = t
      AND   C.ArtId  = @ArtId
     ) *
     (IF t = ANY(@InParagraph) THEN 1 ELSE 0.5)
     * 
     (SELECT SCScore FROM #SCS WHERE TermId = t)
   
   RETURN NEXT t;
END LOOP;

SELECT TOP 4 ArtId 
FROM #tempCalc
SORT BY Score DESC

Outdated Method 2:

SELECT ArtId, 
  SUM(
   SELECT C1.Relevance * C2.Relevance * (IF C1.TID IN @SelectedTerms THEN 1 ELSE 0.5 END IF)
   FROM   Cross AS C1
   LEFT JOIN Cross AS C2 ON C1.TID = C2.TID
   WHERE C1.AID = @ArtId
   AND C1.AID <> C2.AID
  ) AS Score

!! Haven't tested the code yet, since I don't have Postgres here. Will check later. I believe the first query exists already, made by @rubenverboon .