Search results for "Principal Polynomial Analysis"

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PRINCIPAL POLYNOMIAL ANALYSIS

2014

© 2014 World Scientific Publishing Company. This paper presents a new framework for manifold learning based on a sequence of principal polynomials that capture the possibly nonlinear nature of the data. The proposed Principal Polynomial Analysis (PPA) generalizes PCA by modeling the directions of maximal variance by means of curves instead of straight lines. Contrarily to previous approaches PPA reduces to performing simple univariate regressions which makes it computationally feasible and robust. Moreover PPA shows a number of interesting analytical properties. First PPA is a volume preserving map which in turn guarantees the existence of the inverse. Second such an inverse can be obtained…

FOS: Computer and information sciencesPolynomialComputer Networks and CommunicationsComputer scienceMachine Learning (stat.ML)02 engineering and technologyReduction (complexity)03 medical and health sciencessymbols.namesake0302 clinical medicineStatistics - Machine LearningArtificial Intelligence0202 electrical engineering electronic engineering information engineeringPrincipal Polynomial AnalysisPrincipal Component AnalysisMahalanobis distanceModels StatisticalCodingDimensionality reductionNonlinear dimensionality reductionGeneral MedicineClassificationDimensionality reductionManifold learningNonlinear DynamicsMetric (mathematics)Jacobian matrix and determinantsymbolsRegression Analysis020201 artificial intelligence & image processingNeural Networks ComputerAlgorithmAlgorithms030217 neurology & neurosurgeryCurse of dimensionalityInternational Journal of Neural Systems
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Nonlinear data description with Principal Polynomial Analysis

2012

Principal Component Analysis (PCA) has been widely used for manifold description and dimensionality reduction. Performance of PCA is however hampered when data exhibits nonlinear feature relations. In this work, we propose a new framework for manifold learning based on the use of a sequence of Principal Polynomials that capture the eventually nonlinear nature of the data. The proposed Principal Polynomial Analysis (PPA) is shown to generalize PCA. Unlike recently proposed nonlinear methods (e.g. spectral/kernel methods and projection pursuit techniques, neural networks), PPA features are easily interpretable and the method leads to a fully invertible transform, which is a desirable property…

business.industryCodingDimensionality reductionNonlinear dimensionality reductionDiffusion mapSparse PCAComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISIONElastic mapPattern recognitionManifold LearningClassificationKernel principal component analysisComputingMethodologies_PATTERNRECOGNITIONPrincipal component analysisPrincipal Polynomial AnalysisArtificial intelligencePrincipal geodesic analysisbusinessDimensionality ReductionMathematics
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