dc.contributor.author Leznik, M. dc.contributor.author Tofallis, C. dc.date.accessioned 2007-09-26T12:51:42Z dc.date.available 2007-09-26T12:51:42Z dc.date.issued 2005 dc.identifier.citation Leznik , M & Tofallis , C 2005 ' Estimating Invariant Principal Components Using Diagonal Regression ' Business School Working Papers , vol. UHBS 2005-4 , University of Hertfordshire . dc.identifier.other PURE: 120821 dc.identifier.other PURE UUID: d3379080-bda2-4d76-ab8d-b557c7fabea1 dc.identifier.other dspace: 2299/715 dc.identifier.uri http://hdl.handle.net/2299/715 dc.description.abstract In this work we apply the method of diagonal regression to derive an alternative version of Principal Component Analysis (PCA). Diagonal regression was introduced by Ragnar Frisch (the first economics Nobel laureate) in his paper Correlation and Scatter in Statistical Variables (1928). The benefits of using diagonal regression in PCA are that it provides components that are scale-invariant (i.e. changing the units of measurement leads to an equivalent result), and which reflect both the correlation structure of the data set, and the variance structure as well. By contrast PCA based on the correlation matrix will only reflect the correlation structure of the data. The problem is formulated as a generalized eigen-analysis and is demonstrated using a numerical example which highlights some desirable properties of what we call Invariant Principal Components Analysis (IPCA). en dc.language.iso eng dc.publisher University of Hertfordshire dc.relation.ispartofseries Business School Working Papers dc.rights Open dc.title Estimating Invariant Principal Components Using Diagonal Regression en dc.contributor.institution Department of Marketing and Enterprise dc.contributor.institution Hertfordshire Business School dc.contributor.institution Social Sciences, Arts & Humanities Research Institute dc.contributor.institution Centre for Research on Management, Economy and Society dc.contributor.institution Statistical Services Consulting Unit dc.relation.school Hertfordshire Business School dcterms.dateAccepted 2005 rioxxterms.type Working paper herts.preservation.rarelyaccessed true herts.rights.accesstype Open
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