Klasifikacijska stabla

master's thesis

• Author: Anja Damiš
• Mentor: Anamarija Jazbec (mentor)
• Committee member: Anamarija Jazbec (predsjednik povjerenstva)
• Committee member: Bojan Basrak (član povjerenstva)
• Committee member: Vjekoslav Kovač (član povjerenstva)
• Committee member: Pavle Goldstein (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2016-09-26, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Metoda klasifikacijskih stabla temelji se na binarnom stablu. Ako je uvjet pri određenom čvoru zadovoljen, podaci pripadaju lijevoj grani, ako nije pripadaju desnoj grani. Kriteriji prema kojima se postavljaju uvjeti pri čvorovima su mjere nečistoće čvora: klasifikacijska greška, Gini indeks i unakrsna entropija. Od svih mogućih cijepanja, odabire se ono koje postiže najveću redukciju nečistoće čvora, odnosno ono koje ima najbolju kvalitetu cijepanja. Podrezivanje stabla provodi se nakon kreiranja inicijalnog stabla kako bi se izbjegla pretjerana prilagođenost podacima. Od svih mogućih podstabala, odaberemo niz podstabala koristeći cijenu složenosti, a krosvalidacijom procijenimo grešku pojedinog podstabla te odaberemo ono s najnižom ukupnom greškom.

Abstract (english)

The method of classification trees is based on binary tree. If the condition at a particular node is met, the data belong to the left branch, if condition isn’t met, data belong to the right branch. The criteria for the conditions at the nodes are node impurity measures: classification error, Gini index and cross entropy. Of all the possible splittings, we choose the one that achieves the greatest reduction in node impurity, or one that has the best quality of splitting. Pruning the tree is carried out after the initial growing of the tree in order to avoid overfitting of the data. Of all the possible subtrees, we choose a run of subtrees using the cost-complexity criterion and cross-validation error estimation of each subtree and choose the one with the lowest total error.

• Keywords: metoda klasifikacijskih stabla; binarno stablo; mjere nečistoće čvora; klasifikacijska greška; Gini indeks; unakrsna entropija
• Keywords (english): method of classification trees; binary tree; node impurity measures; classification error; Gini index; cross entropy
• Language: croatian
• URN:NBN: urn:nbn:hr:217:158902
• Study programme: Title: Mathematical Statistics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2019-01-08 11:37:54