2021
Doubly Stochastic Normalization of the Gaussian Kernel Is Robust to Heteroskedastic Noise.
Landa B, Coifman RR, Kluger Y. Doubly Stochastic Normalization of the Gaussian Kernel Is Robust to Heteroskedastic Noise. SIAM Journal On Mathematics Of Data Science 2021, 3: 388-413. PMID: 34124607, PMCID: PMC8194191, DOI: 10.1137/20m1342124.Peer-Reviewed Original ResearchStochastic normalizationHeteroskedastic noiseGaussian kernelHigh-dimensional settingsMatrix convergesAmbient dimensionDifferent noise variancesEuclidean spaceData pointsNoise varianceSymmetric normalizationCertain normalizationAffinity matrixClean counterpartsPairwise distancesKernelNoiseData analysis techniqueSingle-cell RNA-sequencing dataParticular directionSpaceWidespread approachConvergesMatrixHeteroskedasticity
2013
Multiscale data sampling and function extension
Bermanis A, Averbuch A, Coifman R. Multiscale data sampling and function extension. Applied And Computational Harmonic Analysis 2013, 34: 15-29. DOI: 10.1016/j.acha.2012.03.002.Peer-Reviewed Original ResearchSequence of approximationsGaussian kernel matrixData pointsAdaptive gridSpecial decompositionMultiscale schemeKernel matrixMultiscale decompositionGaussian kernelInterpolation methodMutual distanceData samplingFine hierarchyExtension methodEmpirical functionHierarchical procedureFunction extensionApproximationExtensionDecompositionPointKernelSchemeSubsamplingGrid