Solving weakly supervised regression problem using low-rank manifold regularization

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.