Search results for "Sparse PCA"

showing 3 items of 3 documents

Sign and Rank Covariance Matrices: Statistical Properties and Application to Principal Components Analysis

2002

In this paper, the estimation of covariance matrices based on multivariate sign and rank vectors is discussed. Equivariance and robustness properties of the sign and rank covariance matrices are described. We show their use for the principal components analysis (PCA) problem. Limiting efficiencies of the estimation procedures for PCA are compared.

Covariance matrixbusiness.industrySparse PCAPattern recognitionCovarianceKernel principal component analysisCorrespondence analysisScatter matrixPrincipal component analysisApplied mathematicsArtificial intelligencebusinessCanonical correlationMathematics
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Feature selection on a dataset of protein families: from exploratory data analysis to statistical variable importance

2016

Proteins are characterized by several typologies of features (structural, geometrical, energy). Most of these features are expected to be similar within a protein family. We are interested to detect which features can identify proteins that belong to a family, as well as to define the boundaries among families. Some features are redundant: they could generate noise in identifying which variables are essential as a fingerprint and, consequently, if they are related or not to a function of a protein family. We defined an original approach to analyze protein features for defining their relationships and peculiarities within protein families. A multistep approach has been mainly performed in R …

Quantitative Biology::Biomoleculesbusiness.industrySparse PCAPattern recognitionFeature selectionLinear discriminant analysisCross-validationRandom forestExploratory data analysisStatistical classificationArtificial intelligencebusinessCluster analysisMathematics
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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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