Jolliffe I. Principal Component Analysis (2ed., Springer, 2002)(518s)
Jolliffe I. Principal Component Analysis (2ed., Springer, 2002)(518s) Jolliffe I. Principal Component Analysis (2ed., Springer, 2002)(518s)
ContentsPreface to the Second EditionPreface to the First EditionAcknowledgmentsList of FiguresList of Tablesvixxvxxiiixxvii1 Introduction 11.1 Definition and Derivation of Principal Components . . . 11.2 A Brief History of Principal Component Analysis .... 62 Properties of Population Principal Components 102.1 Optimal Algebraic Properties of PopulationPrincipal Components ................... 112.2 Geometric Properties of Population Principal Components 182.3 Principal Components Using a Correlation Matrix .... 212.4 Principal Components with Equal and/or Zero Variances 273 Properties of Sample Principal Components 293.1 Optimal Algebraic Properties of SamplePrincipal Components ................... 303.2 Geometric Properties of Sample Principal Components . 333.3 Covariance and Correlation Matrices: An Example . . . 393.4 Principal Components with Equal and/or Zero Variances 43
xviiiContents3.4.1 Example ....................... 433.5 The Singular Value Decomposition ............ 443.6 Probability Distributions for Sample Principal Components 473.7 Inference Based on Sample Principal Components .... 493.7.1 Point Estimation .................. 503.7.2 Interval Estimation ................. 513.7.3 Hypothesis Testing ................. 533.8 Patterned Covariance and Correlation Matrices ..... 563.8.1 Example ....................... 573.9 Models for Principal Component Analysis . ....... 594 Interpreting Principal Components: Examples 634.1 Anatomical Measurements ................. 644.2 TheElderlyatHome .................... 684.3 Spatial and Temporal Variation in Atmospheric Science . 714.4 Properties of Chemical Compounds ............ 744.5 StockMarketPrices..................... 765 Graphical Representation of Data UsingPrincipal Components 785.1 Plotting Two or Three Principal Components ...... 805.1.1 Examples ...................... 805.2 PrincipalCoordinateAnalysis ............... 855.3 Biplots ............................ 905.3.1 Examples ...................... 965.3.2 Variations on the Biplot .............. 1015.4 Correspondence Analysis .................. 1035.4.1 Example ....................... 1055.5 Comparisons Between Principal Components andotherMethods........................ 1065.6 Displaying Intrinsically High-Dimensional Data ..... 1075.6.1 Example ....................... 1086 Choosing a Subset of Principal Components or Variables 1116.1 How Many Principal Components? ............ 1126.1.1 Cumulative Percentage of Total Variation .... 1126.1.2 Size of Variances of Principal Components .... 1146.1.3 The Scree Graph and the Log-Eigenvalue Diagram 1156.1.4 The Number of Components with Unequal Eigenvaluesand Other Hypothesis Testing Procedures 1186.1.5 Choice of m Using Cross-Validatory or ComputationallyIntensive Methods ............. 1206.1.6 Partial Correlation ................. 1276.1.7 Rules for an Atmospheric Science Context .... 1276.1.8 Discussion ...................... 130
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xviiiContents3.4.1 Example ....................... 433.5 The Singular Value Decomposition ............ 443.6 Probability Distributions for Sample <strong>Principal</strong> <strong>Component</strong>s 473.7 Inference Based on Sample <strong>Principal</strong> <strong>Component</strong>s .... 493.7.1 Point Estimation .................. 503.7.2 Interval Estimation ................. 513.7.3 Hypothesis Testing ................. 533.8 Patterned Covariance and Correlation Matrices ..... 563.8.1 Example ....................... 573.9 Models for <strong>Principal</strong> <strong>Component</strong> <strong>Analysis</strong> . ....... 594 Interpreting <strong>Principal</strong> <strong>Component</strong>s: Examples 634.1 Anatomical Measurements ................. 644.2 TheElderlyatHome .................... 684.3 Spatial and Temporal Variation in Atmospheric Science . 714.4 Properties of Chemical Compounds ............ 744.5 StockMarketPrices..................... 765 Graphical Representation of Data Using<strong>Principal</strong> <strong>Component</strong>s 785.1 Plotting Two or Three <strong>Principal</strong> <strong>Component</strong>s ...... 805.1.1 Examples ...................... 805.2 <strong>Principal</strong>Coordinate<strong>Analysis</strong> ............... 855.3 Biplots ............................ 905.3.1 Examples ...................... 965.3.2 Variations on the Biplot .............. 1015.4 Correspondence <strong>Analysis</strong> .................. 1035.4.1 Example ....................... 1055.5 Comparisons Between <strong>Principal</strong> <strong>Component</strong>s andotherMethods........................ 1065.6 Displaying Intrinsically High-Dimensional Data ..... 1075.6.1 Example ....................... 1086 Choosing a Subset of <strong>Principal</strong> <strong>Component</strong>s or Variables 1116.1 How Many <strong>Principal</strong> <strong>Component</strong>s? ............ 1126.1.1 Cumulative Percentage of Total Variation .... 1126.1.2 Size of Variances of <strong>Principal</strong> <strong>Component</strong>s .... 1146.1.3 The Scree Graph and the Log-Eigenvalue Diagram 1156.1.4 The Number of <strong>Component</strong>s with Unequal Eigenvaluesand Other Hypothesis Testing Procedures 1186.1.5 Choice of m Using Cross-Validatory or ComputationallyIntensive Methods ............. 1206.1.6 Partial Correlation ................. 1276.1.7 Rules for an Atmospheric Science Context .... 1276.1.8 Discussion ...................... 130
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