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i CONTENTS Page Table of Contents i Abstract ii 1. INTRODUCTION 1.1 Multivariate Biomedical Data 1.2 Biomedical Cancer Genomic Data 1.3 Microarray and Gene Expression Levels 1.4 Data Under Study 1.4.1 Leukemia Cancer Gene Expression Data Set 1.5 Objectives of the Project 1.6 Summary Statistics for Multivariate Data Set 1.7 Relative Variance Covariance Matrix. 1 1 3 4 6 8 10 12 13 2. EXPLORATORY DATA ANALYSIS 2.1 Histograms 2.2 Box and Whiskers Plots 2.3 Transformations 2.3.1 Box-Cox Transformation 2.4 Exploratory Data Analysis: A Graphical View 2.5 Probability Plots 2.6 Fitting a Probability Distribution 2.7 Extreme Value Distributions 2.7.1 Extreme Value Distribution Argument 2.7.2 Generalized Extreme Value Distributions 2.7.3 Gumbel Distribution 2.7.4 Fréchet Distribution 2.7.5 Weibull Distribution 2.8 Goodness of Fit Test 2.9 Probability Difference Plots 2.10 Correlation Structure of the Data Matrix 2.10.1 Interpreting Coefficient of Correlation 17 17 18 19 20 21 32 35 36 37 38 40 42 43 45 56 60 61 3. PRINCIPAL COMPONENT ANALYSIS AND ITS USE IN CLUSTERING TISSUE SAMPLES 3.1 Clustering Gene Expression Data 3.2 Cluster Analysis: A Comparison 3.3 Principal Component Analysis and Clustering 3.4 Principal Component Analysis 3.5 Principal Components 3.5.1 Principal Components Using Variance Covariance Matrix 3.5.2 Principal Components Using Correlation Matrix 3.5.3 Principal Components Using Relative Variance Matrix 3.6 Principal Components : Relative Variance Matrix versus Correlation Matrix 3.7 Principal Component Loadings 68 69 71 74 76 77 77 79 81 82 83
