20.500.12556/RUL-161316 Problem matričnih napolnitev preko optimizacije na Riemannovih mnogoterostih Matrix Completion Problem Through Optimization on Riemannian Manifolds V diplomski nalogi obravnavamo problem matričnih napolnitev, pri katerem je cilj obnoviti manjkajoče vrednosti v matriki na podlagi razpoložljivih podatkov in minimizirati rang matrike. Osredotočimo se na algoritem, ki temelji na tehnikah Riemannovih mnogoterosti. V delu implementiramo algoritem, predstavljen v članku "Low-rank matrix completion by Riemannian optimization", in ga preizkusimo v kakovosti rekonstrukcije na sintetičnih podatkih in različnih slikovnih podatkih z dodanimi motnjami, šumom ali manjkajočimi piksli. Rezultate analiziramo in interpretiramo s pomočjo matematičnega ozadja algoritma. In this thesis, we address the problem of matrix completion, where the goal is to recover missing values in a matrix based on the available data and minimizing the rank of the matrix. We focus on an algorithm that relies on Riemannian manifold techniques. In the work, we implement the algorithm presented in the paper "Low-rank matrix completion by Riemannian optimization" and test its reconstruction quality on synthetic data and on various image data with added disturbances, noise, or missing pixels. The results are then analyzed and interpreted with the help of the mathematical background of the algorithm. matrične napolnitve Riemannove mnogoterosti optimizacija minimizacija ranga rekonstrukcija slik matrix completion Riemannian manifolds optimization rank minimization image reconstruction true false false Slovenski jezik Angleški jezik Diplomsko delo/naloga 2024-09-09 15:20:32 2024-09-09 15:20:34 2024-10-15 07:27:14 0000-00-00 00:00:00 2024 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 37290 211501827 Poklukar_Ana_-_Problem_matricnih_napolnitev_preko_optimizacije_na_Riemannovih_mnogoterostih.pdf Poklukar_Ana_-_Problem_matricnih_napolnitev_preko_optimizacije_na_Riemannovih_mnogoterostih.pdf 1 2B0F61250A42FA8D95A8701D52F64EE3 d894f7411c0fe98ccd3988469fa3a98b596cc4f00545c4a8a22767453082db41 431c16ba-6eae-11ef-b232-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=190219 Fakulteta za računalništvo in informatiko 0 0 0