Personalized recommender systems take advantage of users past history to make predictions. The cold start problem concerns the personalized recommendations for users with no or few past history (new users). Providing recommendations to users with small past history becomes a difficult problem for CF models because their learning and predictive ability is limited. Multiple research have been conducted in this direction using hybrid models. These models use auxiliary information (multimodal information, side information, etc.) to overcome the cold start problem.
Cold start problem is that problem, where system is not able to recommend items to users. For every recommender system, its required to build user profile by considering her preferences and likes. User profile is developed by considering her activities and behaviours she perform with the system. On the basis of user previous history and activities system make decisions and recommend items consequently. The problem arises when a new user or new item enters the system, for such user/items system don't have enough information to make a decision. For example, a new user has not rated some items and not yet visited/viewed some items then it would be difficult for the system to build a model on that basis. Cold start problem arisis in three different situation i.e. for new users, for new items and for new community. To solve this issue different solutions have been suggested an article please have a look.
*Recommender Systems: Issues, Challenges, and Research Opportunities.
If we talking about a new item for online shopping, I think the system should have the ability to recommend this item based on whoever liked or purchase any other items similar in the same category. For example, if this item is a new movie (action movie), the RS should recommend it for any users who like action movies before. As for new user , since there is no history, RS should depend on the way this new user navigates the web site and analysis his/her behavior to see which items is possible that this new user might be interesting for. I have read an article about How Long Do Users Stay on Web Pages. It's summary that users often leave Web pages in 10-20 seconds if they are lost interest . Based on the time the user spent on particular page, if it is more than 20 sec, this means this user maybe like some items on that page.
For online shopping you can use navigation history to build a user profile. As far as new user is concerned, this problem can be solved by looking at the navigation (Implicit feedback approach) and activities user perform. in recommender systems this approach is declared as implicit feedback mechanism for getting user feedback and updating user profile. You can also build user profile by looking at the time she spends on a particular item, page. Moreover, you can fix this by observing user viewing and downloading information. Other solution could be asking user to provide ratings for certain items, this way you can build her profile. Also, you can get her contextual information by using her IP address and find trend of users in that particular area, location, institution to which this user belongs.
On the other hand, for new product, you should look at the category of that product and should calculate aggregate ratings for that item on the basis of category at which this item belongs. This way you can predict ratings for such new products.