  Parameter prediction is essential for many applications, facilitating
insightful interpretation and decision-making. However, in many real life
domains, such as power systems, medicine, and engineering, it can be very
expensive to acquire ground truth labels for certain datasets as they may
require extensive and expensive laboratory testing. In this work, we introduce
a semi-supervised learning approach based on topological projections in
self-organizing maps (SOMs), which significantly reduces the required number of
labeled data points to perform parameter prediction, effectively exploiting
information contained in large unlabeled datasets. Our proposed method first
trains SOMs on unlabeled data and then a minimal number of available labeled
data points are assigned to key best matching units (BMU). The values estimated
for newly-encountered data points are computed utilizing the average of the $n$
closest labeled data points in the SOM's U-matrix in tandem with a topological
shortest path distance calculation scheme. Our results indicate that the
proposed minimally supervised model significantly outperforms traditional
regression techniques, including linear and polynomial regression, Gaussian
process regression, K-nearest neighbors, as well as deep neural network models
and related clustering schemes.
