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master's thesis
Kanoničke korelacije
2020. urn:nbn:hr:126:688497
Kovačić, Ela
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Pure Mathematics and Mathematics Teaching
Probability, Mathematical Statistics and Data Science Research Group

Cite this document

Kovačić, E. (2020). Kanoničke korelacije (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:688497

Kovačić, Ela. "Kanoničke korelacije." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2020. https://urn.nsk.hr/urn:nbn:hr:126:688497

Kovačić, Ela. "Kanoničke korelacije." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2020. https://urn.nsk.hr/urn:nbn:hr:126:688497

Kovačić, E. (2020). 'Kanoničke korelacije', Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 01 April 2025, https://urn.nsk.hr/urn:nbn:hr:126:688497

Kovačić E. Kanoničke korelacije [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2020 [cited 2025 April 01] Available at: https://urn.nsk.hr/urn:nbn:hr:126:688497

E. Kovačić, "Kanoničke korelacije", Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2020. Available at: https://urn.nsk.hr/urn:nbn:hr:126:688497

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Metadata
TitleKanoničke korelacije
Title (english)Canonical Correlation
AuthorEla Kovačić
MentorMirta Benšić (mentor)
Committee memberNenad Šuvak (predsjednik povjerenstva)
Committee memberMirta Benšić (član povjerenstva)
Committee memberDanijel Grahovac (član povjerenstva)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
(Chair of Pure Mathematics and Mathematics Teaching)
(Probability, Mathematical Statistics and Data Science Research Group)
Osijek
Defense date and country2020-02-04, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Probability Theory and Statistics
Abstract
Kanonička korelacija jedna je od procedura za objašnjavanje povezanosti između dva skupa varijata. Potrebno je pronaći linearne kombinacije varijata tako da je njihova korelacija maksimalna. Parovi čija je korelacija maksimalna, te nisu u korelaciji s ostalim linearnim kombinacijama nazivamo kanoničke varijate, a njihovu korelaciju nazivamo kanonička korelacija. Koeficijenti kojim se postiže maksimalna korelacija nazivaju se kanonički koeficijenti. Može se proučavati i povezanost između ... More varijabli originalnog vektora i kanoničke varijate, te dobivene vrijednosti nazivamo kanonička opterećenja. Također, proučava se i veza između originalne varijate i suprotne kanoničke varijate, što se naziva kanonička kros-opterećenja. Kanoničke korelacije i kanoničke koeficijente dobivamo računanjem svojstvenih vrijednosti i svojstvenih vektora. Tako su pozitivni korijeni svojstvenih vrijednosti tražene kanoničke korelacije, a svojstveni vektori traženi kanonički koeficijenti. S obzirom da većina podataka nije iste varijabilnosti, potrebno je standardizirati podatke. Algebra korištena za računanje kanoničkih koeficijenata i kanoničke korelacije koristi se i za računanje njihovih procjena iz podataka. U primjeru smo proučavali vezu između dvije varijate, od kojih prvi varijat sadrži psihološke karakteristike osobe, a drugi akademske karakteristike osobe te interpretiramo dobivene rezultate. Za interpretaciju koristimo prvi par kanoničkih varijata s obzirom da je njihova korelacija najveća, i statistički značajna. Less
Abstract (english)
Canonical correlation is one of the procedures for explaining the relationship between the two sets of variates. The procedure is consisted of finding the linear combinations of variables that have the maximal correlation. The pairs that have the maximal correlation, but are not correlated with other linear combinations, are called canonical variates, while the correlation between the canonical variates is called the canonical correlation. Coefficients that maximize the correlation are... More the canonical coefficients. It is possible to study the relationship between the variables of the original vector and the canonical variate, where the obtained values are called canonical loadings. The correlation between variables of the original vector and the opposite canonical variate, which is called the canonical cross-loadings, can also be studied. As for the canonical correlations and canonical coefficients, they are obtained by the computing of eigenvalues and eigenvectors, so that the positive square roots of eigenvalue are canonical correlation, and eigenvectors are canonical coefficients. Given that the majority of data are not of the same variability, it is necessary to standardize them. Algebra used to calculate canonical coefficients and canonical correlations was also applied in the calculation of their estimates. The example included in this thesis studies the relationship between two variates. The first variate contains the psychological characteristics of the person, and the second is consisted of the academic characteristics. The first pair of canonical variates is used for the interpretation of the obtained results, since their correlation is the largest and statistically significant. Less
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:688497
Study programmeTitle: Mathematics; specializations in: Financial and Statistical Mathematics, Mathematics and Computer Science, Industrial and Applied Mathematics
Course: Financial and Statistical Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2020-02-05 10:44:59
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