2015
Information Integration, Organization, and Numerical Harmonic Analysis
Coifman R, Talmon R, Gavish M, Haddad A. Information Integration, Organization, and Numerical Harmonic Analysis. 2015, 254-271. DOI: 10.1002/9781118853887.ch10.Peer-Reviewed Original ResearchPartial differential equationsHarmonic analysisLocal linear modelsLocal similarity modelNumerical harmonic analysisDifferential equationsMathematical frameworkNewtonian calculusGlobal solutionClassical toolsFunctional regressionLinear modelData matrixUnrelated approachesMathematicsSignal processingNumericsEquationsMachine learningGraphGlobal configurationCalculusData analysisGeometryModel
2014
Quantitative Arbor Analytics: Unsupervised Harmonic Co-Clustering of Populations of Brain Cell Arbors Based on L-Measure
Lu Y, Carin L, Coifman R, Shain W, Roysam B. Quantitative Arbor Analytics: Unsupervised Harmonic Co-Clustering of Populations of Brain Cell Arbors Based on L-Measure. Neuroinformatics 2014, 13: 47-63. PMID: 25086878, DOI: 10.1007/s12021-014-9237-2.Peer-Reviewed Original ResearchConceptsCo-clustering methodAnalytics systemSynthetic datasetsThree-dimensional visualizationAnalysis ToolkitHeterogeneous ensembleDistance measureAlgorithmMultivariate data pointsData smoothingData pointsWavelet basisData matrixHarmonic analysis theoryL-measureNeuroMorpho databaseDatasetAnalysis theoryToolkitVisualizationEnsembleRobustnessDatabaseSuperiorityMethod
2011
Harmonic Analysis of Digital Data Bases
Coifman R, Gavish M. Harmonic Analysis of Digital Data Bases. Applied And Numerical Harmonic Analysis 2011, 161-197. DOI: 10.1007/978-0-8176-8095-4_9.Peer-Reviewed Original ResearchSpace of matricesData matrixData pointsEntropy conditionTensor productLaplacian eigenvectorsPotential operatorsDistribution geometryIterative procedureHarmonic analysisGraph oneAffinity graphLocal geometryEfficient reconstructionEigenvectorsGeometryData analysis methodsOperatorsGraphHaar-like basesMatrixAnalysis methodPartition treeExpansion coefficientVertices