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I have a data set which consists of users and products purchased by them. But, I don't have any ratings for each of the purchased products.

I am trying to use item-item collaborative filtering recommendation using Apache mahout. But without ratings I am not sure how accurate the recommendation will be.

Is there a way out to to recommend data to users? What I had done till now is provide the purchased item as 1 rating.

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Yes, the case when no explicit ratings are provided by users is called the "implicit feedback" setting. In this case, user generated events (like viewing or buying products) are collected for training, which implicitly contain user preference (that is, a user expresses interest in a product by viewing it, but not necessarily "likes" it after all).

As the implicit feedback case is much more common in real life scenarios, than the explicit feedback case, there is a huge amount of literature around it with very sophisticated algorithms. On the other hand, setting $preference=1$ and using an explicit algorithm is not a bad start.

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