Analiza podatkov z metodo delnih najmanjših kvadratov (PLS metoda) : delo diplomskega seminarja

Trojer, Žiga (author), Knez, Marjetka (mentor)

V delu diplomskega seminarja definiramo linearne modele več spremenljivk v splošnem. Nato predstavimo model po metodi najmanjših kvadratov, kjer si ogledamo glavne značnilnosti modela in izpostavimo glavne pomankljivosti za različne tipe podatkov. Nadaljujemo s predstavitvijo sorodnega modela regresije glavnih komponent, kjer predstavimo glavne ideje metode glavnih komponent. Ko smo seznanjeni z delovanjem te metode, podoben princip uporabimo na metodi delnih najmanjših kvadratov. Teorijo modela podkrepimo s primeri delovanja metode v napovedovanju vrednosti spremenljivk. Nato se dotaknemo še problema klasifikacije in nelinearnih modelov, kjer delovanje prikažemo z enostavnima zgledoma.

• Language: Slovenian
• Keywords: delni najmanjši kvadrati, NIPALS, regresija, klasifikacija, redukcija dimenzij
• Work type: Final seminar paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2019
• PID: 20.500.12556/RUL-110091
• UDC: 519.2
• COBISS.SI-ID: 18741081
• Publication date in RUL: 12.09.2019

TROJER, Žiga, 2019, Analiza podatkov z metodo delnih najmanjših kvadratov (PLS metoda) : delo diplomskega seminarja [online]. Bachelor’s thesis. [Accessed 14 April 2025]. Retrieved from: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=eng&id=110091

Secondary language

• Language: English
• Title: Data Analysis Using the Partial Least Squares Method (PLS method)

Abstract

In the seminar, we define linear models of several variables in general. Then we introduce the model using the least squares method, where we look at the main features of the model and highlight the main disadvantages for different types of data. We continue to introduce a related model of principal component regression, where we present the main ideas of the principal component method. After we are familiar with how this method works, we apply a similar principle to the method of partial least squares. The theory of the model is supported by examples of how the method works in prediction. Finally we look also at the problem of classification and nonlinear models, where we show the operation on some simple examples.

• Keywords: partial least squares, NIPALS, regression, classification, dimensionality reduction