delo diplomskega seminarja
Jan Rudof (Author), Marjetka Krajnc (Mentor)

Abstract

V diplomski nalogi se osredotočimo na izpeljavo metode podpornih vektorjev. Najprej se lotimo matematične izpeljave za linearno ločljive podatke, za katere lahko najdemo optimalno ločitveno hiperravnino, ki nam vedno loči podatke v dva razreda. Model nato razširimo na linearno neločljive podatke, kjer pride do problema, saj ni možno najti hiperravnine, ki bi nam optimalno ločila podatke v dva razreda. Uvedemo kazenske spremenljivke in raven šuma, s katerim nadziramo napačno grupirane podatke in tako dovolimo nekaterim podatkom, da padejo v napačni razred. Metodo lahko uporabimo tudi na nelinearnih podatkih, pri čemer moramo za izračun optimalne ločitvene hiperravnine definirati nove funkcije, imenovane jedra. Metodo podpornih vektorjev nato uporabimo na praktičnem primeru. Uporabimo zgodovinske podatke vrednosti delnic 34 tehnoloških podjetij, na katere apliciramo metodo podpornih vektorjev za napovedovanje vrednosti delnic v nekem trenutku v prihodnosti. Napovemo lahko, ali bo vrednost delnice narasla ali padla. S pomočjo te metode nato izračunamo verjetnosti pravilnih napovedi.

Keywords

finančna matematika;metoda podpornih vektorjev;klasifikacijska funkcija;mejni pas;napovedovanje vrednosti delnic;jedra;

Data

Language: Slovenian
Year of publishing:
Typology: 2.11 - Undergraduate Thesis
Organization: UL FMF - Faculty of Mathematics and Physics
Publisher: [J. Rudof]
UDC: 519.8
COBISS: 18816857 Link will open in a new window
Views: 1221
Downloads: 280
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Other data

Secondary language: English
Secondary title: Support vector machines for data grouping and regression
Secondary abstract: In this thesis we focus on derivation of the support vector machines. We begin with a mathematical derivation for linearly separable data, where we can easily find the optimal separable hyperplane that always separates the data into two classes. We then extend our model to linearly inseparable data, where the problem occurs since it is not possible to find a hyperplane that optimally separates the data into two classes. For this reason we introduce penalty variables and a cost parameter by which we control wrongly clustered data, thus allowing some data to fall into the wrong class. The method can also be used on nonlinear data, where we define new functions, called kernels, to calculate the optimal separation hyperplane. The support vector machines is further used in the practical example. We use historical stock's values of 34 technology companies, on which we apply the support vector machine method to predict the stock's values at a certain point in the future. In our case, we can only predict whether the stock's value will rise or fall. Using the presented method, we can then calculate probabilities of correct forecasts.
Secondary keywords: support vector machines;classification function;margin;stock forecasting;kernel functions;
Type (COBISS): Final seminar paper
Study programme: 0
Embargo end date (OpenAIRE): 1970-01-01
Thesis comment: Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Finančna matematika - 1. stopnja
Pages: 32 str.
ID: 11223585