APPLICATION OF SINGULAR VALUE DECOMPOSITION IN PRINCIPAL COMPONENT ANALYSIS

APPLICATION OF SINGULAR VALUE DECOMPOSITION IN PRINCIPAL COMPONENT ANALYSIS

Rapid technologicaladvancementsdemandefficiencyinextractingvitalinfor- mation fromlarge-scaledata.Dimensionreductionmethods,suchasprincipal component analysis(PCA),playacrucialroleinsimplifyingdatacomplexity to facilitateeasierinterpretationandanalysiswhileenhancingcomputational efficiency.PCAis...

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Bibliographic Details
Main Author: Agung Tanzali, Levana
Format: Final Project
Language:Indonesia
Online Access:https://digilib.itb.ac.id/gdl/view/83544
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Institution: Institut Teknologi Bandung
Language: Indonesia
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Summary:Rapid technologicaladvancementsdemandefficiencyinextractingvitalinfor- mation fromlarge-scaledata.Dimensionreductionmethods,suchasprincipal component analysis(PCA),playacrucialroleinsimplifyingdatacomplexity to facilitateeasierinterpretationandanalysiswhileenhancingcomputational efficiency.PCAiseffectiveinreducingdatadimensions,aimingtodecrease complexitywhilemaintainingsignificantvariancesothattheessentialinformation within thedataisstillwell-represented.Conventionally,PCAisperformedthrough the decompositionofthecovariancematrix.However,PCAcanalsobeimple- mented throughsingularvaluedecomposition(SVD),whichoffersadvantagesin efficiencyandnumericalstability.ThisthesisdiscussesthePCAmethodandits relationship withSVD,alongwithexamplesofitsapplicationtorealdata.Applying SVD toPCAyieldstwoinformations.First,newaxesareestablishedthatformthe basis foranewcoordinatesystem.Second,theprincipalcomponentscores,which are theprojectionsoftheoriginaldataontothenewcoordinatesystem.

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