Hi dear

If you are using collaborative filtering in a online system and an item is removed, it's better to that item from rating matrix too, but because of preventing negative side effect of this process on similarity of user-user or item-user prediction, it's better to remove this item after a while, now if this item ranked many times, it's better to remove that so long later and if it has less rates, you could remove it soon. I think it's better to use a distribution formula for remove time based on number of rates of that item.

Sincerely

Removing the data *will* make your user-to-user algorithm *less accurate* (compromised is far too strong a term).  Given that there are no real disadvantages to keeping the data (other than negligible space and processing time), it should be kept.  You can easily mark the item as no longer available and use that to prevent it from being displayed.

However, even if you were to remove the data, it certainly should not cause any sort of problems due to "a gap in the matrix".  Anyone who claims that doesn't know what they are talking about.

Dear Mark Waser, and Bezed Soleimani,

Thanks for your attention.

1- Let's suppose that we have an online e-commerce service, like Amazon.

2- In the store, we have different items.

3- Each item has an unique ID.

4- For each item, we get only one instance (i.e Quantity of each item = 1)

Suppose also that we have a user-based collaborative recommender, so we have :

1- A table of items

2- A table of users

3- and Matrix user-item-rating, to save the rating R given by user U on item I.

So, because of the fact that we have only one instance for each item (Qte(item)=1), if one user buy this item, the quantity beacome = 0 (i.e. the item is no more available).

Can the collaborative filtering work in this circumstances ?

I will make an example to better illustrate a case:

We have :

Item1 (Quantity = 1)

Item2 (Quantity = 1)

Item3 (Quantity = 1)

Item4 (Quantity = 1)

And we have:

User1, User2

Let's consider that a positive rate is implicitly done when a user purchase an item.

If User1 purchase Item1

and User2 purchase Item2

This means that User1 and User2 noted positively (implicitly) Item1, Item2, respectively. And we insert ratings into the matrix (e.g: U11=+1 , U22 = +1).

At this stage (after purchases), we have:

Item1 (Quantity = 0)

Item2 (Quantity = 0)

Item3 (Quantity = 1)

Item4 (Quantity = 1)

Now we have two possibilities:

1- Either maintain the items 1 and 2, with flags indicating that the items 1 and 2 are no more available,

2- Or Delete them.

1- In the first possibility:

Maitaining these items suggest that their rating vector, in the matrix, will be used in the item-based algorithm. Ok, but the problem is that the only person who rated the item 1 was the user1, and the only person who rated the item2 was the user2.

And by the way, we lose the fundementals of the collaboration, because we cannot find any neighbours.

I would say, that the collaboration algorithm has no sense in such scenario. Do you agree ?

Yes dear Mohamed, and because of such influence, I said it's better to remove it but suppose the initial quantity of items was 2 or 3, therefor maybe rating matrix be like this:

        I1              I2          I3

U1:  1               0           1

U2:  0               1           1

if initial quantity of items was 2, now I3 is finished and we have no more, but in rating matrix it is showing a neighborhood between U1 and U2 then if you remove it when quantity of I3=0, then you remove neighborhood of U1 and U2 too! But if you keep it, when U3 register in website, he/she never buy I3 because we don't have anymore, so the gap of I3 for new users in rating matrix cause to reduce accuracy of recommendation system in long time.

So I suggest don't remove I3 from rating matrix just in time it quantity equals to zero, but don't keep it forever, for example remove it after a month from rating matrix. If you want to use collaborating system in applied system, I think this type of removing help you to better maintain your website too and prevent to deal with large scale data in rating matrix too.

I hope could explain enough and helpful for you and dear Mark

Sincerely

So . . . . your problem is your data schema . . . . the max quantity of 1 effectively claims that everything is unique which makes the concept of comparison nonsensical and  literally impossible.

I'm not quite sure *why* you have a table of items (Amazon certainly doesn't) but that is not what you should be running your recommender off of.  You should be running it off of an itemTYPE table (which would be a foreign key for your items table if such is truly necessary) -- which is pretty much what Behzad suggested.

Dear Mark Waser, and Bezed Soleimani,

Thank you for your suggestions.

Yes Mark, i'm in a scenario where everything is unique. 

For example, consider a web site where content is provided by users (Like amazon).

So, i think that every item, provided by user, is unique, do you agree ? every item has a unique ID. And because the collaborative approach uses only the ID, this makes it difficult.

In such scenario i prefer to use content-based approach. But i'm curious to know how we can deal with such problem.

Thank you.

Dear Mohamed

Instead of using content based approach, you can just categorize items and recommend based on Category ID instead of Item ID. I think it's a simple and application approach. Basically, content based approach try to extract content by topic modeling and such approaches that seems all of them want to extract some feature from items that one of these feature could be category. If you can simply categorize or classify your items, you could use this approach. It seems you don't want to research on collaborative filtering approaches and have a novelty for publishing paper, if you want to implement a re commander system for business, I think this idea could help you, even though it could be basic of a novel approach too, if it's not publish yet :)

With Regards 

Ok, thanks all for your contribution.