Collaborative Filtering: Non-Personalized item-to-item similarity

Question

I'm trying to compute item-to-item similarity along the lines of Amazon's "Customers who viewed/purchased X have also viewed/purchased Y and Z". All of the examples and references I've seen are for either computing item similarity for ranked items, for finding user-user similarity, or for finding recommended items based on the current users' history. I'd like to start off with a non-targeted approach before factoring in the current users' preferences.

Looking at the Amazon.com recommendations white paper, they use the following logic for offline item-item similarity:

For each item in product catalog, I1 
  For each customer C who purchased I1
    For each item I2 purchased by customer C
       Record that a customer purchased I1 and I2
  For each item I2 
    Compute the similarity between I1 and I2

If I understand correctly, by the time we're at "Compute similiarty between I1 and I2", I have a list of items(I2) purchased in conjunction with a single value I1(the outer loop).

How is this calculation performed?

Another idea is that I'm overthinking this and making it more difficult than I need to - Would it be enough to do a top-n query on the count of I2 bought in conjunction with I1?

I also appreciate suggestions on whether or not this approach is a correct one. My product database has about 150k items at any time. Since the bulk of the reading material I've seen shows user-item similarity or even user-user similarity, should I be looking to go that route instead.

I've worked with similarity algorithms in the past but they've always involved a rank or a score. I think the only way this would work would be to build a customer-product matrix scoring 0/1 for not purchased/purchased. Given the purchase history and the item size, this could get really large.

edit: although i listed python as a tag, i'd prefer to keep the logic inside of a db, preferably using Oracle PL/SQL.

Answer 1

There's a good O'Reilly book on this topic. While the whitepaper might lay the logic out in pseudo-code like that, I don't think that approach would scale very well. The calculations are all probability calculations, so things like Bayes' Theorem get used to say, "Given Person A purchased X, what's the likelihood they purchased Z?" Straightforward looping over the data is working too hard. You have to go through it all for each person.