Posplošena diskriminantna analiza z uporabo posplošenega singularnega razcepa

delo diplomskega seminarja

Jernej Banevec (Author), Marjetka Krajnc (Mentor)

Abstract

Linearna diskriminantna analiza je metoda, ki se uporablja v statistiki, pri strojnem učenju in pri metodah prepoznavanja vzorcev. Njen cilj je poiskati takšno kombinacijo merjenih spremenljivk, ki kar najbolje ločuje med vnaprej določenimi razredi. Definirana je kot optimizacijski problem, ki vključuje kovariančne matrike, ki zadoščajo pogoju nesingularnosti. Ker ta pogoj otežuje aplikativnost metode, predstavimo posplošitev linearne diskriminantne analize, ki je uporabna tudi v primeru, ko navadna linearna diskriminantna analiza odpove. Uporabo posplošene diskriminantne analize preizkusimo na primeru iz področja medicine, kjer v razrede razvrščamo merjene podatke.

Keywords

matematika;linearna diskriminantna analiza;posplošeni singularni razcep;optimizacija sledi;

Data

Language:	Slovenian
Year of publishing:	2019
Typology:	2.11 - Undergraduate Thesis
Organization:	UL FMF - Faculty of Mathematics and Physics
Publisher:	[J. Banevec]
UDC:	512
COBISS:	18717529
Views:	1818
Downloads:	175
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Generalized discriminant analysis using the generalized singular value decomposition
Secondary abstract:	Linear discriminant analysis is a method used in statistics, machine learning and pattern recognition. Its aim is to find a combination of features that separates between pre-structured clusters. It is defined as an optimization problem involving covariance matrices, that have to be nonsingular. Since this condition makes it difficult to apply the method on every data, we aim to generalize linear discriminant analysis and make it useful also in cases, when classic linear discriminant analysis fails. Usage of generalized discriminant analysis is shown on medical case of cluster prediction.
Secondary keywords:	mathematics;linear discriminant analysis;generalized singular value decomposition;trace optimization;
Type (COBISS):	Final seminar paper
Study programme:	0
Thesis comment:	Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Finančna matematika - 1. stopnja
Pages:	29 str.
ID:	11216341