Your question consists of two parts: (A) How to work with new users and elements and (B) how to work with new interactions (for example, ratings, clicks, etc.).
(A) There are basically two different strategies for working with new users and elements (regardless of whether we use matrix factorization or something else):
- assessment of user / subject characteristics from user attributes (demography, polls) or attribute (price, genre, text description, categories)
- active learning: displaying new elements to all users interacting with the system, or certain elements for new users of the system, so as to balance the individual user interface and receive information from the system.
There are many articles in the scientific literature on both issues.
(B) This is really not problematic - incremental updates of the matrix factorization model do not have high computational costs. See, for example, this article: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.165.8010&rep=rep1&type=pdf
MyMediaLite library (disclaimer: I'm the main author) supports incremental updates for several matrix factorization methods: http://ismll.de/mymedialite
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