Metode podpornih vektorjev

delo diplomskega seminarja

Lenart Treven (Author), Matija Pretnar (Mentor), Jan Kralj (Co-mentor)

Abstract

V delu predstavimo metode podpornih vektorjev, njihovo matematično izpeljavo in praktično uporabo. Izpeljemo primarni problem, ki ga dobimo, ko želimo linearno ločljive dvorazredne podatke ločiti s hiperravnino. Dani problem posplošimo na dvorazredne podatke, ki niso linearno ločljivi. Predstavimo teorijo dualnosti konveksnih optimizacijskih problemov, s pomočjo katere dokažemo krepki izrek o dualnosti za konveksne probleme. Primarni problem prevedemo na njegov dual. V dualni problem uvedemo jedrne funkcije. Dokažemo, da sta polinomsko in radialno jedro skalarna produkta. Pokažemo, kako ravnamo v primeru, ko imamo večrazredne podatke. Pokažemo način, kako ocenimo natančnost klasifikatorja s prečnim preverjanjem. Pokažemo delovanje različnih jeder na preprostih dvorazsežnih podatkih, ki jih vzamemo iz podatkovne množice IRIS. Metode podpornih vektorjev naučimo na večji podatkovni množici ter pokažemo, na kakšen način izberemo končni napovedni model.

Keywords

matematika;metode podpornih vektorjev;dualni problem;jedra;

Data

Language:	Slovenian
Year of publishing:	2018
Typology:	2.11 - Undergraduate Thesis
Organization:	UL FMF - Faculty of Mathematics and Physics
Publisher:	[L. Treven]
UDC:	517
COBISS:	18429273
Views:	862
Downloads:	302
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Support vector machines
Secondary abstract:	In this work we present support vector machines, their mathematical derivation and practical usage. The primal problem, which we encounter while trying to separate two-class data with hyperplane, is described. We generalise given primal problem to nonlinear separable data. The theory of convex optimization is introduced which helps us to prove strong duality in the convex case. We convert the primal problem to its dual. Kernel functions are introduced into the dual problem. We prove that the polynomial and radial kernels are scalar products in some space. The problem of multiclass data is described. Methods such as cross-validation are introduced for error estimation. Different kernels are demonstrated on a simple two dimensional data set, which is a part of the IRIS data set. Support vector machines are trained on a bigger data set and an indication of a possible way of choosing final model is shown.
Secondary keywords:	mathematics;support vector machines;dual problem;kernel functions;
Type (COBISS):	Final seminar paper
Study programme:	0
Thesis comment:	Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Matematika - 1. stopnja
Pages:	41 str.
ID:	10958187