PRINCIPAL COMPONENT ANALYSIS
CONTENTS INTRODUCTION DE?NITION AND DERIVATION OF PRINCIPAL COMPONENTS A BRIEF HISTORY OF PRINCIPAL COMPONENT ANALYSIS PROPERTIES OF POPULATION PRINCIPAL COMPONENTS OPTIMAL ALGEBRAIC PROPERTIES OF POPULATION PRINCIPAL COMPONENTS GEOMETRIC PROPERTIES OF POPULATION PRINCIPAL COMPONENTS PRINCIPAL COMPONENTS USING A CORRELATION MATRIX PRINCIPAL COMPONENTS WITH EQUAL AND/OR ZERO VARIANCES PROPERTIES OF SAMPLE PRINCIPAL COMPONENTS OPTIMAL ALGEBRAIC PROPERTIES OF SAMPLE PRINCIPAL COMPONENTS GEOMETRIC PROPERTIES OF SAMPLE PRINCIPAL COMPONENTS COVARIANCE AND CORRELATION MATRICES: AN EXAMPLE EXAMPLE THE SINGULAR VALUE DECOMPOSITION PROBABILITY DISTRIBUTIONS FOR SAMPLE PRINCIPAL COMPONENTS INFERENCE BASED ON SAMPLE PRINCIPAL COMPONENTS POINT ESTIMATION INTERVAL ESTIMATION HYPOTHESIS TESTING PATTERNED COVARIANCE AND CORRELATION MATRICES MODELS FOR PRINCIPAL COMPONENT ANALYSIS INTERPRETING PRINCIPAL COMPONENTS: EXAMPLES ANATOMICAL MEASUREMENTS THE ELDERLY AT HOME SPATIAL AND TEMPORAL VARIATION IN ATMOSPHERIC SCIENCE PROPERTIES OF CHEMICAL COMPOUNDS STOCK MARKET PRICES GRAPHICAL REPRESENTATION OF DATA USING PRINCIPAL COMPONENTS PLOTTING TWO OR THREE PRINCIPAL COMPONENTS EXAMPLES PRINCIPAL COORDINATE ANALYSIS BIPLOTS VARIATIONS ON THE BIPLOT CORRESPONDENCE ANALYSIS COMPARISONS BETWEEN PRINCIPAL COMPONENTS AND OTHER METHODS DISPLAYING INTRINSICALLY HIGH-DIMENSIONAL DATA CHOOSING A SUBSET OF PRINCIPAL COMPONENTS OR VARIABLES HOW MANY PRINCIPAL COMPONENTS? CUMULATIVE PERCENTAGE OF TOTAL VARIATION SIZE OF VARIANCES OF PRINCIPAL COMPONENTS THE SCREE GRAPH AND THE LOG-EIGENVALUE DIAGRAM THE NUMBER OF COMPONENTS WITH UNEQUAL EIGEN- VALUES AND OTHER HYPOTHESIS TESTING PROCEDURES CHOICE OF M USING CROSS-VALIDATORY OR COMPUTA- TIONALLY INTENSIVE METHODS PARTIAL CORRELATION RULES FOR AN ATMOSPHERIC SCIENCE CONTEXT DISCUSSION CHOOSING M, THE NUMBER OF COMPONENTS: EXAMPLES CLINICAL TRIALS BLOOD CHEMISTRY GAS CHROMATOGRAPHY DATA SELECTING A SUBSET OF VARIABLES EXAMPLES ILLUSTRATING VARIABLE SELECTION ALATE ADELGES (WINGED APHIDS) CRIME RATES PRINCIPAL COMPONENT ANALYSIS AND FACTOR ANALYSIS MODELS FOR FACTOR ANALYSIS ESTIMATION OF THE FACTOR MODEL COMPARISONS BETWEEN FACTOR AND PRINCIPAL COMPONENT ANALYSIS AN EXAMPLE OF FACTOR ANALYSIS CONCLUDING REMARKS PRINCIPAL COMPONENTS IN REGRESSION ANALYSIS PRINCIPAL COMPONENT REGRESSION SELECTING COMPONENTS IN PRINCIPAL COMPONENT REGRESSION CONNECTIONS BETWEEN PC REGRESSION AND OTHER METHODS VARIATIONS ON PRINCIPAL COMPONENT REGRESSION VARIABLE SELECTION IN REGRESSION USING PRINCIPAL COMPO- NENTS FUNCTIONAL AND STRUCTURAL RELATIONSHIPS EXAMPLES OF PRINCIPAL COMPONENTS IN REGRESSION PITPROP DATA HOUSEHOLD FORMATION DATA PRINCIPAL COMPONENTS USED WITH OTHER MULTIVARIATE TECHNIQUES DISCRIMINANT ANALYSIS CLUSTER ANALYSIS PROJECTION PURSUIT MIXTURE MODELS CANONICAL CORRELATION ANALYSIS AND RELATED TECHNIQUES CANONICAL CORRELATION ANALYSIS EXAMPLE OF CCA MAXIMUM COVARIANCE ANALYSIS (SVD ANALYSIS), REDUNDANCY ANALYSIS AND PRINCIPAL PREDICTORS OTHER TECHNIQUES FOR RELATING TWO SETS OF VARIABLES 10 OUTLIER DETECTION, IN?UENTIAL OBSERVATIONS AND ROBUST ESTIMATION DETECTION OF OUTLIERS USING PRINCIPAL COMPONENTS 10 1 1 EXAMPLES IN?UENTIAL OBSERVATIONS IN A PRINCIPAL COMPONENT ANALYSIS 10 2 1 EXAMPLES SENSITIVITY AND STABILITY ROBUST ESTIMATION OF PRINCIPAL COMPONENTS 11 ROTATION AND INTERPRETATION OF PRINCIPAL COMPONENTS ROTATION OF PRINCIPAL COMPONENTS 11 1 1 EXAMPLES 11 1 2 ONE-STEP PROCEDURES USING SIMPLICITY CRITERIA ALTERNATIVES TO ROTATION 11 2 1 COMPONENTS WITH DISCRETE-VALUED COE?CIENTS 11 2 2 COMPONENTS BASED ON THE LASSO 11 2 3 EMPIRICAL ORTHOGONAL TELECONNECTIONS 11 2 4 SOME COMPARISONS SIMPLI?ED APPROXIMATIONS TO PRINCIPAL COMPONENTS 11 3 1 PRINCIPAL COMPONENTS WITH HOMOGENEOUS, CONTRAST AND SPARSITY CONSTRAINTS PHYSICAL INTERPRETATION OF PRINCIPAL COMPONENTS 12 PCA FOR TIME SERIES AND OTHER NON-INDEPENDENT DATA PCA AND ATMOSPHERIC TIME SERIES 12 2 1 SINGULAR SPECTRUM ANALYSIS (SSA) 12 2 2 PRINCIPAL OSCILLATION PATTERN (POP) ANALYSIS 12 2 3 HILBERT (COMPLEX) EOFS 12 2 4 MULTITAPER FREQUENCY DOMAIN-SINGULAR VALUE DECOMPOSITION (MTM SVD) 12 2 5 CYCLO-STATIONARY AND PERIODICALLY EXTENDED EOFS (AND POPS) 12 2 6 EXAMPLES AND COMPARISONS FUNCTIONAL PCA 12 3 1 THE BASICS OF FUNCTIONAL PCA (FPCA) 12 3 2 CALCULATING FUNCTIONAL PCS (FPCS) 12 3 3 EXAMPLE - 100 KM RUNNING DATA 12 3 4 FURTHER TOPICS IN FPCA PCA AND NON-INDEPENDENT DATA—SOME ADDITIONAL TOPICS 12 4 1 PCA IN THE FREQUENCY DOMAIN 12 4 2 GROWTH CURVES AND LONGITUDINAL DATA 12 4 3 CLIMATE CHANGE—FINGERPRINT TECHNIQUES 12 4 4 SPATIAL DATA 12 4 5 OTHER ASPECTS OF NON-INDEPENDENT DATA AND PCA 13 PRINCIPAL COMPONENT ANALYSIS FOR SPECIAL TYPES OF DATA PRINCIPAL COMPONENT ANALYSIS FOR DISCRETE DATA ANALYSIS OF SIZE AND SHAPE PRINCIPAL COMPONENT ANALYSIS FOR COMPOSITIONAL DATA 13 3 1 EXAMPLE: 100 KM RUNNING DATA PRINCIPAL COMPONENT ANALYSIS IN DESIGNED EXPERIMENTS COMMON PRINCIPAL COMPONENTS PRINCIPAL COMPONENT ANALYSIS IN THE PRESENCE OF MISSING DATA PCA IN STATISTICAL PROCESS CONTROL SOME OTHER TYPES OF DATA 14 GENERALIZATIONS AND ADAPTATIONS OF PRINCIPAL COMPONENT ANALYSIS NON-LINEAR EXTENSIONS OF PRINCIPAL COMPONENT ANALYSIS 14 1 1 NON-LINEAR MULTIVARIATE DATA ANALYSIS—GI?AND RELATED APPROACHES 14 1 2 ADDITIVE PRINCIPAL COMPONENTS AND PRINCIPAL CURVES 14 1 3 NON-LINEARITY USING NEURAL NETWORKS 14 1 4 OTHER ASPECTS OF NON-LINEARITY WEIGHTS, METRICS, TRANSFORMATIONS AND CENTERINGS 14 2 1 WEIGHTS 14 2 2 METRICS 14 2 3 TRANSFORMATIONS AND CENTERING PCS IN THE PRESENCE OF SECONDARY OR INSTRUMENTAL VARIABLES PCA FOR NON-NORMAL DISTRIBUTIONS 14 4 1 INDEPENDENT COMPONENT ANALYSIS THREE-MODE, MULTIWAY AND MULTIPLE GROUP PCA MISCELLANEA 14 6 1 PRINCIPAL COMPONENTS AND NEURAL NETWORKS 14 6 2 PRINCIPAL COMPONENTS FOR GOODNESS-OF-FIT STATIS- TICS 14 6 3 REGRESSION COMPONENTS, SWEEP-OUT COMPONENTS AND EXTENDED COMPONENTS 14 6 4 SUBJECTIVE PRINCIPAL COMPONENTS