  We solve a weakly supervised regression problem. Under "weakly" we understand
that for some training points the labels are known, for some unknown, and for
others uncertain due to the presence of random noise or other reasons such as
lack of resources. The solution process requires to optimize a certain
objective function (the loss function), which combines manifold regularization
and low-rank matrix decomposition techniques. These low-rank approximations
allow us to speed up all matrix calculations and reduce storage requirements.
This is especially crucial for large datasets. Ensemble clustering is used for
obtaining the co-association matrix, which we consider as the similarity
matrix. The utilization of these techniques allows us to increase the quality
and stability of the solution. In the numerical section, we applied the
suggested method to artificial and real datasets using Monte-Carlo modeling.
