Posplošena diskriminantna analiza z uporabo posplošenega singularnega razcepa : delo diplomskega seminarja

Banevec, Jernej (author), Knez, Marjetka (mentor)

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.

• Language: Slovenian
• Keywords: Linearna diskriminantna analiza, posplošeni singularni razcep, optimizacija sledi
• Work type: Final seminar paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2019
• PID: 20.500.12556/RUL-109533
• UDC: 512
• COBISS.SI-ID: 18717529
• Publication date in RUL: 05.09.2019

BANEVEC, Jernej, 2019, Posplošena diskriminantna analiza z uporabo posplošenega singularnega razcepa : delo diplomskega seminarja [online]. Bachelor’s thesis. [Accessed 27 August 2025]. Retrieved from: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=eng&id=109533

Secondary language

• Language: English
• Title: Generalized discriminant analysis using the generalized singular value decomposition

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.

• Keywords: Linear discriminant analysis, generalized singular value decomposition, trace optimization