In this paper, we propose a study on the use of weighted topological learning and matrix factorization methods to transform the representation space of a sparse dataset in order to increase the quality of learning, and adapt it to the case of transfer learning. The matrix factorization allows us to find latent variables, weighted topological learning is used to detect the most relevant among them. New data representation is based on their projections on the weighted topological model. Each object in the dataset is described by a new representation consisting of the distances of this object to all components of the topological model (prototypes).