How to select similar sets in SQL

Question

I have the following tables:

Order
----
ID (pk)

OrderItem
----
OrderID (fk -> Order.ID)
ItemID (fk -> Item.ID)
Quantity

Item
----
ID (pk)
         


        

Answer 1

This approach takes into account the Quantity using the Extended Jaccard Coefficient or Tanimoto Similarity. It computes the similarity across all Orders, by using a the vector of common ItemIDs of magnitude Quantity. It does cost a table scan, but doesn't require an N^2 computation of all possible similarities.

SELECT
    OrderID,
    SUM(v1.Quantity * v2.Quantity) /
    (SUM(v1.Quantity * v1.Quantity) +
     SUM(v2.Quantity * v2.Quantity) -
     SUM(v1.Quantity * v2.Quantity) ) AS coef
FROM
    OrderItem v1 FULL OUTER JOIN OrderItem v2
    ON v1.ItemID = v2.ItemID
    AND v2.OrderID = ?
GROUP BY OrderID
HAVING coef > 0.85;

Formula for the Extended Jaccard Coefficient: