Exploratory Data Analysis with MATLAB, Second Edition (Chapman & Hall CRC Computer Science & Data Analysis)

499 Pages·2010·6.43 MB·English

by  Wendy L. Martinez

Exploratory Data Analysis
with MATLAB®
Second Edition
Chapman & Hall/CRC
Computer Science and Data Analysis Series
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Approach and Bioinformatics
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Computational Statistics Handbook with
MATLAB®, Second Edition Microarray Image Analysis:
Wendy L. Martinez and Angel R. Martinez An Algorithmic Approach
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Fionn Murtagh Data Mining
Sankar K. Pal and Pabitra Mitra
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Experiments R Graphics
Kai-Tai Fang, Runze Li, and Agus Sudjianto Paul Murrell
Exploratory Data Analysis with MATLAB®, R Programming for Bioinformatics
Second Edition Robert Gentleman
Wendy L. Martinez, Angel R. Martinez,
Semisupervised Learning for Computational
and Jeffrey L. Solka
Linguistics
Exploratory Multivariate Analysis by Steven Abney
Example Using R
Statistical Computing with R
François Husson, Sébastien Lê, and Maria L. Rizzo
Jérôme Pagès
Exploratory Data Analysis
with MATLAB®
Second Edition
Wendy L. Martinez
Angel R. Martinez
Jeffrey L. Solka
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Library of Congress Cataloging‑in‑Publication Data
Martinez, Wendy L.
Exploratory data analysis with MATLAB / Wendy L. Martinez, Angel Martinez,
Jeffrey Solka. -- 2nd ed.
p. cm. -- (Chapman & Hall/CRC computer science and data analysis series)
Includes bibliographical references and index.
ISBN 978-1-4398-1220-4 (hardback)
1. Multivariate analysis. 2. MATLAB. 3. Mathematical statistics. I. Martinez, Angel
R. II. Solka, Jeffrey L., 1955- III. Title.
QA278.M3735 2010
519.5’35--dc22 2010044042
Visit the Taylor & Francis Web site at
http://www.taylorandfrancis.com
and the CRC Press Web site at
http://www.crcpress.com
Angel and Wendy dedicate this book totheir children:
Deborah,
Jeffrey,
Robbi (the middlechild),
andLisa (Principessa)
Jeffrey dedicates this book to his wife Beth,
sons Stephen andRob,and
future daughter-in-law Rebecca
Table of Contents
PrefacetotheSecondEdition...........................................................................xiii
PrefacetotheFirstEdition...............................................................................xvii
Part I
IntroductiontoExploratoryDataAnalysis
Chapter 1
IntroductiontoExploratoryDataAnalysis
1.1WhatisExploratoryDataAnalysis .............................................................3
1.2OverviewoftheText .....................................................................................6
1.3AFewWordsaboutNotation ......................................................................8
1.4DataSetsUsedintheBook ...........................................................................9
1.4.1UnstructuredTextDocuments ........................................................9
1.4.2GeneExpressionData .....................................................................12
1.4.3OronsayDataSet .............................................................................18
1.4.4SoftwareInspection .........................................................................19
1.5TransformingData .......................................................................................20
1.5.1PowerTransformations ..................................................................21
1.5.2Standardization................................................................................22
1.5.3SpheringtheData ............................................................................24
1.6FurtherReading ...........................................................................................25
Exercises ..............................................................................................................27
Part II
EDAasPattern Discovery
Chapter 2
DimensionalityReduction (cid:151)LinearMethods
2.1Introduction ..................................................................................................31
2.2PrincipalComponentAnalysis(cid:151)PCA ....................................................33
2.2.1PCAUsingtheSampleCovarianceMatrix .................................34
2.2.2PCAUsingtheSampleCorrelationMatrix .................................37
2.2.3HowManyDimensionsShouldWeKeep? .................................38
2.3SingularValueDecomposition(cid:151)SVD ....................................................42
2.4NonnegativeMatrixFactorization ............................................................47
vii
viii ExploratoryDataAnalysiswithMATLABfi,2nd Edition
2.5FactorAnalysis .............................................................................................51
2.6Fisher(cid:146)sLinearDiscriminant ......................................................................56
2.7IntrinsicDimensionality..............................................................................61
2.7.1NearestNeighborApproach .........................................................63
2.7.2CorrelationDimension ...................................................................67
2.7.3MaximumLikelihoodApproach ..................................................68
2.7.4EstimationUsingPackingNumbers ............................................70
2.8SummaryandFurtherReading .................................................................72
Exercises ..............................................................................................................73
Chapter 3
DimensionalityReduction (cid:151)NonlinearMethods
3.1MultidimensionalScaling(cid:151)MDS ............................................................79
3.1.1MetricMDS ......................................................................................81
3.1.2NonmetricMDS ...............................................................................91
3.2ManifoldLearning .......................................................................................99
3.2.1LocallyLinearEmbedding .............................................................99
3.2.2IsometricFeatureMapping(cid:151)ISOMAP ....................................101
3.2.3HessianEigenmaps .......................................................................103
3.3ArtificialNeuralNetworkApproaches ..................................................108
3.3.1Self-OrganizingMaps ...................................................................108
3.3.2GenerativeTopographicMaps ....................................................111
3.3.3CurvilinearComponentAnalysis ...............................................116
3.4SummaryandFurtherReading ...............................................................121
Exercises ............................................................................................................122
Chapter 4
DataTours
4.1GrandTour .................................................................................................126
4.1.1TorusWindingMethod ................................................................127
4.1.2PseudoGrandTour .......................................................................129
4.2InterpolationTours ....................................................................................132
4.3ProjectionPursuit .......................................................................................134
4.4ProjectionPursuitIndexes ........................................................................142
4.4.1PosseChi-SquareIndex ................................................................142
4.4.2MomentIndex ................................................................................145
4.5IndependentComponentAnalysis .........................................................147
4.6SummaryandFurtherReading ...............................................................151
Exercises ............................................................................................................152
Chapter 5
FindingClusters
5.1Introduction ................................................................................................155
5.2HierarchicalMethods ................................................................................157
TableofContents ix
5.3OptimizationMethods(cid:151)k-Means .........................................................163
5.4SpectralClustering .....................................................................................167
5.5DocumentClustering ................................................................................171
5.5.1NonnegativeMatrixFactorization(cid:151)Revisited .......................173
5.5.2ProbabilisticLatentSemanticAnalysis ......................................177
5.6EvaluatingtheClusters .............................................................................182
5.6.1RandIndex .....................................................................................182
5.6.2CopheneticCorrelation ................................................................185
5.6.3UpperTailRule..............................................................................186
5.6.4SilhouettePlot ................................................................................189
5.6.5GapStatistic....................................................................................191
5.7SummaryandFurtherReading ...............................................................197
Exercises ............................................................................................................200
Chapter 6
Model-BasedClustering
6.1OverviewofModel-BasedClustering ....................................................205
6.2FiniteMixtures ...........................................................................................207
6.2.1MultivariateFiniteMixtures ........................................................210
6.2.2ComponentModels(cid:151)ConstrainingtheCovariances ............211
6.3Expectation-MaximizationAlgorithm ....................................................217
6.4HierarchicalAgglomerativeModel-BasedClustering .........................222
6.5Model-BasedClustering............................................................................224
6.6MBCforDensityEstimationandDiscriminantAnalysis ....................231
6.6.1IntroductiontoPatternRecognition ...........................................231
6.6.2BayesDecisionTheory..................................................................232
6.6.3EstimatingProbabilityDensitieswithMBC..............................235
6.7GeneratingRandomVariablesfromaMixtureModel.........................239
6.8SummaryandFurtherReading ...............................................................241
Exercises ............................................................................................................244
Chapter 7
SmoothingScatterplots
7.1Introduction ................................................................................................247
7.2Loess.............................................................................................................248
7.3RobustLoess ...............................................................................................259
7.4ResidualsandDiagnosticswithLoess ....................................................261
7.4.1ResidualPlots .................................................................................261
7.4.2SpreadSmooth ...............................................................................265
7.4.3LoessEnvelopes(cid:151)UpperandLowerSmooths .......................268
7.5SmoothingSplines .....................................................................................269
7.5.1RegressionwithSplines................................................................270
7.5.2SmoothingSplines .........................................................................272
7.5.3SmoothingSplinesforUniformlySpacedData ........................278
7.6ChoosingtheSmoothingParameter .......................................................281
x ExploratoryDataAnalysiswithMATLABfi,2nd Edition
7.7BivariateDistributionSmooths ................................................................285
7.7.1PairsofMiddleSmoothings.........................................................285
7.7.2PolarSmoothing ............................................................................287
7.8CurveFittingToolbox ...............................................................................291
7.9SummaryandFurtherReading ...............................................................293
Exercises ............................................................................................................294
Part III
GraphicalMethodsforEDA
Chapter 8
VisualizingClusters
8.1Dendrogram ................................................................................................301
8.2Treemaps .....................................................................................................303
8.3RectanglePlots ...........................................................................................306
8.4ReClusPlots ................................................................................................312
8.5DataImage ..................................................................................................317
8.6SummaryandFurtherReading ...............................................................323
Exercises ............................................................................................................324
Chapter 9
Distribution Shapes
9.1Histograms ..................................................................................................327
9.1.1UnivariateHistograms .................................................................327
9.1.2BivariateHistograms ....................................................................334
9.2Boxplots .......................................................................................................336
9.2.1TheBasicBoxplot ..........................................................................337
9.2.2VariationsoftheBasicBoxplot ....................................................342
9.3QuantilePlots .............................................................................................347
9.3.1ProbabilityPlots ............................................................................347
9.3.2Quantile-QuantilePlot ..................................................................349
9.3.3QuantilePlot ..................................................................................352
9.4Bagplots .......................................................................................................354
9.5RangefinderBoxplot ..................................................................................356
9.6SummaryandFurtherReading ...............................................................359
Exercises ............................................................................................................361
Chapter 10
MultivariateVisualization
10.1GlyphPlots................................................................................................365
10.2Scatterplots ................................................................................................366
10.2.12-Dand3-DScatterplots.............................................................368
10.2.2ScatterplotMatrices .....................................................................371
10.2.3ScatterplotswithHexagonalBinning .......................................372