magistrsko delo
Anamarija Mijatović (Author), Marjetka Krajnc (Mentor)

Abstract

Umetne nevronske mreže so računalniški sistemi, ki delujejo podobno kot nevroni v človeških možganih. Ker so se odlično izkazale kot orodje za prepoznavo skritih vzorcev in korelaciji v podatkih, se uporabljajo za reševanje različnih kompleksnih problemov. V magistrskem delu so obravnavane nevronske mreže z uporabo B-zlepkov, ki pa so zelo uporabni v teoriji aproksimacije. V začetnih poglavjih magistrskega dela je predstavljena polinomska interpolacija in odsekoma polinomske funkcije. V nadaljevanju spoznamo še umetne nevronske mreže, njihovo delovanje in težave, ki se lahko zgodijo v procesu učenja umetnih nevronskih mrež. Sledi implementacija umetnih nevronskih mrež in implementacija B-zlepkov v umetnih nevronskih mrežah. V magistrskem delu so nevronske mreže uporabljene za napovedovanje cene delnice podjetja Microsoft. Ker je v splošnem cena delnice odvisna od veliko faktorjev, je težko doseči natančno napoved. Cilj magistrskega dela je raziskati, ali so umetne nevronske mreže in nevronske mreže z B-zlepki primerne za napovedovanje časovnih vrst in ali z B-zlepki izboljšamo delovanje umetnih nevronskih mrež. V magistrskem delu so B-zlepki v nevronskih mrežah uporabljeni v aktivacijskih funkcijah. Natančneje, aktivacijsko funkcijo nevronske mreže določa zlepek, ki ga tvorimo s pomočjo baznih zlepkov. Za primerjavo rezultatov so v magistrskem delu uporabljene tudi regularne nevronske mreže, pri katerih za aktivacijsko funkcijo izberemo sigmoidno, hiperbolični tangens, ali pa ReLU funkcijo.

Keywords

B-zlepki;nevronske mreže;interpolacija;strojno učenje;metoda vzvratnega razširjanja;metoda gradientnega spusta;

Data

Language: Slovenian
Year of publishing:
Typology: 2.09 - Master's Thesis
Organization: UL FMF - Faculty of Mathematics and Physics
Publisher: [A. Mijatović]
UDC: 519.6
COBISS: 83865091 Link will open in a new window
Views: 714
Downloads: 102
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Other data

Secondary language: English
Secondary title: B-splines in neural networks
Secondary abstract: Artificial neural networks are computing systems that work much like the neurons in the human brain. Neural networks have proven to be an excellent tool for identifying hidden patterns and correlations in data. Because of that, they are used to solve various complex problems. The master's thesis analyzes B-splines artificial neural networks. The initial chapters present polynomial interpolation and piecewise polynomial functions. In the following, we learn about artificial neural networks, their functions and problems that can occur in the process of training artificial neural networks. This is followed by the implementation of artificial neural networks and the implementation of B-splines in artificial neural networks. In the master's thesis neural networks are used for predicting Microsoft stock price based on previous stock prices. Since stock price, in general, depends on many factors, it is difficult to achieve accurate forecast. The thesis aims to investigate whether artificial neural networks and neural networks with B-splines are suitable for predicting time series and whether B-splines improve the performance of artificial neural networks. In the master's thesis, B-splines in neural networks are implemented as activation functions. Specifically, for the activation function, we used a spline that is formed from B-splines. Also, regular neural networks with sigmoid, hyperbolic tangent or ReLU activation function are implemented, with which we compare the obtained results.
Secondary keywords: B-splines;neural networks;interpolation;machine learning;backpropagation;gradient descent method;
Type (COBISS): Master's thesis/paper
Study programme: 0
Thesis comment: Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Finančna matematika - 2. stopnja
Pages: X, 54 str.
ID: 13797461