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Most recommendation algorithms recommend new products to users.

If you bought this you might like that

But sometimes the item user is most likely to buy is an item that he bought sometime ago.

Is there any algorithm appropriate for this use?

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Usually recommendation algorithms provides the confidence that a user will like an item. Items that the user already bought should get high confidence - the user bought them since he liked them.

In most cases filtering out item the user already bough is done in the application level, not in the algorithm level.

So , you can use regular recommendation algorithms in order to know if the user will like the item.

Please note that you might face a different problem - will the user buy the item for the second/third time. In order to cope with this problem, using some domain knowledge might be beneficial. If the products are usually bough many times (e.g., milk), just use the recommendation algorithm. If all the products have the same tendency to be bought few times, build a model for that (e.g., probability for buying another time given already buying x times) and combine the models. If your products are very different from this aspect you might need to get into a lower level. Different domains require different solution but you might split the product by the buying behavior and train few recommendation systems, add the number of buying as a feature, etc.

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What you are actually looking for is a technique called Content-Based Filtering
As Wikipedia defines it:

Another common approach when designing recommender systems is content-based filtering. Content-based filtering methods are based on a description of the item and a profile of the user’s preference. In a content-based recommender system, keywords are used to describe the items and a user profile is built to indicate the type of item this user likes. In other words, these algorithms try to recommend items that are similar to those that a user liked in the past (or is examining in the present). In particular, various candidate items are compared with items previously rated by the user and the best-matching items are recommended. This approach has its roots in information retrieval and information filtering research.

More can be found Here.

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