The use of mixture regression in machine learningMlakar, Peter (Avtor) Oblak, Polona (Mentor) Nummi, Tapio (Komentor) mixture modelsregressionnatural cubic splinesclusteringRegression and clustering are important components of machine learning. The first servers as a tool for discovering relations between dependent and independent variables in a dataset. With the second, data can be ordered in clusters or group, depending on the similarities between individual data entries. In our thesis, we investigate a novel algorithm that conducts both tasks at the same time. The algorithm for non-parametric regression, which is based on Gaussian mixed models, discovers cluster in longitudinal datasets and, with the help of non-parametric regression, creates smooth mean development curves for those clusters. In the proposed algorithm, the non-parametric regression is based on natural cubic spline regression. We present the theoretical basis for the algorithm and its components. We also incorporate approaches to reduce the proposed algorithms computational complexity. An implementation of the proposed algorithm and corresponding speed-ups are constructed in the programming language Julia. The algorithms performance is demonstrated quantitatively on a synthetic and qualitatively on a real dataset. A Covid-19 dataset available from the World Health Organization was utilized in the later evaluation. The goal of this evaluation is to group together countries with similar epidemiological development trends.20212021-09-10 15:40:00Magistrsko delo/naloga130170sl