Research in random forest algorithms able to switch data sets
Semi-Supervised Learning

The combination of unsupervised learning and supervised learning is referred to as semi-supervised learning, which is the concept that I believe you are searching for.

Label propagation is often cited when outlining the heuristics of semi-supervised learning.  The essence is to employ clustering, but to use a tiny set of known cases in order to derive (or propogate) the labels of the clusters.  Hence one is able to use a small set of labeled cases to classify a much larger set of unsupervised data.

Here are some references:


Wikipedia has an entry on the semi-supervised learning.
The scikit learn User Guide is often a useful starting point and has a label propogation routine.
There are, in fact, papers treating semi-supervised random forest models. 
Another one here


Hope this helps!