Horvath Weighted Network Analysis

Applications in Genomics and Systems Biology
1. Auflage 2011
ISBN: 978-1-4419-8819-5
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 421 Seiten

High-throughput measurements of gene expression and genetic marker data facilitate systems biologic and systems genetic data analysis strategies. Gene co-expression networks have been used to study a variety of biological systems, bridging the gap from individual genes to biologically or clinically important emergent phenotypes.

Autoren/Hrsg.

Horvath, Steve

Inhaltsverzeichnis

1;Preface;8
2;Acknowledgements;12
3;Contents;16
4;Acronyms;24
5;Chapter 1: Networks and Fundamental Concepts;26
5.1;1.1 Network Adjacency Matrix ;26
5.1.1;1.1.1 Connectivity and Related Concepts;27
5.1.2;1.1.2 Social Network Analogy: Affection Network;27
5.2;1.2 Analysis Tasks Amenable to Network Methods;28
5.3;1.3 Fundamental Network Concepts;29
5.3.1;1.3.1 Matrix and Vector Notation;30
5.3.2;1.3.2 Scaled Connectivity;30
5.3.3;1.3.3 Scale-Free Topology Fitting Index;31
5.3.4;1.3.4 Network Heterogeneity;33
5.3.5;1.3.5 Maximum Adjacency Ratio;33
5.3.6;1.3.6 Network Density;34
5.3.7;1.3.7 Quantiles of the Adjacency Matrix;35
5.3.8;1.3.8 Network Centralization;35
5.3.9;1.3.9 Clustering Coefficient;36
5.3.10;1.3.10 Hub Node Significance;36
5.3.11;1.3.11 Network Significance Measure;37
5.3.12;1.3.12 Centroid Significance and Centroid Conformity;37
5.3.13;1.3.13 Topological Overlap Measure;38
5.3.14;1.3.14 Generalized Topological Overlap for Unweighted Networks;39
5.3.15;1.3.15 Multinode Topological Overlap Measure;41
5.4;1.4 Neighborhood Analysis in PPI Networks;43
5.4.1;1.4.1 GTOM Analysis of Fly Protein–Protein Interaction Data;43
5.4.2;1.4.2 MTOM Analysis of Yeast Protein–Protein Interaction Data;45
5.5;1.5 Adjacency Function Based on Topological Overlap;46
5.6;1.6 R Functions for the Topological Overlap Matrix;46
5.7;1.7 Network Modules;47
5.8;1.8 Intramodular Network Concepts;49
5.9;1.9 Networks Whose Nodes Are Modules;50
5.10;1.10 Intermodular Network Concepts;51
5.11;1.11 Network Concepts for Comparing Two Networks;52
5.12;1.12 R Code for Computing Network Concepts;54
5.13;1.13 Exercises;55
5.14;References;57
6;Chapter 2:Approximately Factorizable Networks;60
6.1;2.1 Exactly Factorizable Networks;60
6.2;2.2 Conformity for a Non-Factorizable Network;61
6.2.1;2.2.1 Algorithm for Computing the Node Conformity;62
6.3;2.3 Module-Based and Conformity-Based Approximation of a Network;64
6.4;2.4 Exercises;67
6.5;References;68
7;Chapter 3: Different Types of Network Concepts;69
7.1;3.1 Network Concept Functions;70
7.2;3.2 CF-Based Network Concepts;72
7.3;3.3 Approximate CF-Based Network Concepts;73
7.4;3.4 Fundamental Network Concepts Versus CF-Based Analogs;74
7.5;3.5 CF-Based Concepts Versus Approximate CF-Based Analog;75
7.6;3.6 Higher Order Approximations of Fundamental Concepts;76
7.7;3.7 Fundamental Concepts Versus Approx. CF-Based Analogs;77
7.8;3.8 Relationships Among Fundamental Network Concepts;78
7.8.1;3.8.1 Relationships for the Topological Overlap Matrix;79
7.9;3.9 Alternative Expression of the Factorizability F(A);80
7.10;3.10 Approximately Factorizable PPI Modules;80
7.11;3.11 Studying Block Diagonal Adjacency Matrices;85
7.12;3.12 Approximate CF-Based Intermodular Network Concepts;87
7.13;3.13 CF-Based Network Concepts for Comparing Two Networks;88
7.14;3.14 Discussion;89
7.15;3.15 R Code;91
7.16;3.16 Exercises;93
7.17;References;98
8;Chapter 4:Adjacency Functions and Their Topological Effects;100
8.1;4.1 Definition of Important Adjacency Functions;100
8.2;4.2 Topological Effects of the Power Transformation AFpower;102
8.2.1;4.2.1 Studying the Power AF Using Approx. CF-Based Concepts;103
8.2.2;4.2.2 MAR Is a Nonincreasing Function of ß;103
8.3;4.3 Topological Criteria for Choosing AF Parameters;105
8.4;4.4 Differential Network Concepts for Choosing AF Parameters;106
8.5;4.5 Power AF for Calibrating Weighted Networks;107
8.6;4.6 Definition of Threshold-Preserving Adjacency Functions;107
8.7;4.7 Equivalence of Network Construction Methods;109
8.8;4.8 Exercises;110
8.9;References;112
9;Chapter 5: Correlation and Gene Co-Expression Networks;113
9.1;5.1 Relating Two Numeric Vectors;113
9.1.1;5.1.1 Pearson Correlation;115
9.1.2;5.1.2 Robust Alternatives to the Pearson Correlation;116
9.1.3;5.1.3 Biweight Midcorrelation;117
9.1.4;5.1.4 C-Index;118
9.2;5.2 Weighted and Unweighted Correlation Networks;119
9.2.1;5.2.1 Social Network Analogy: Affection Network;120
9.3;5.3 General Correlation Networks;121
9.4;5.4 Gene Co-Expression Networks;123
9.5;5.5 Mouse Tissue Gene Expression Data from of an F2 Intercross;125
9.6;5.6 Overview of Weighted Gene Co-Expression Network Analysis;130
9.7;5.7 Brain Cancer Network Application;132
9.8;5.8 R Code for Studying the Effect of Thresholding;134
9.9;5.9 Gene Network (Re-)Construction Methods;136
9.10;5.10 R Code;137
9.11;5.11 Exercises;139
9.12;References;140
10;Chapter 6: Geometric Interpretation of Correlation Networks Using the Singular Value Decomposition;144
10.1;6.1 Singular Value Decomposition of a Matrix datX;144
10.1.1;6.1.1 Signal Balancing Based on Right Singular Vectors;145
10.1.2;6.1.2 Eigenvectors, Eigengenes, and Left Singular Vectors;146
10.2;6.2 Characterizing Approx. Factorizable Correlation Networks;147
10.3;6.3 Eigenvector-Based Network Concepts;150
10.3.1;6.3.1 Relationships Among Density Concepts in Correlation Networks;152
10.4;6.4 Eigenvector-Based Approximations of Intermodular Concepts;153
10.5;6.5 Networks Whose Nodes are Correlation Modules;155
10.6;6.6 Dictionary for Fundamental-Based and Eigenvector-Based Concepts;156
10.7;6.7 Geometric Interpretation;157
10.7.1;6.7.1 Interpretation of Eigenvector-Based Concepts;157
10.7.2;6.7.2 Interpretation of a Correlation Network;158
10.7.3;6.7.3 Interpretation of the Factorizability;159
10.8;6.8 Network Implications of the Geometric Interpretation;160
10.8.1;6.8.1 Statistical Significance of Network Concepts;161
10.8.2;6.8.2 Intramodular Hubs Cannot be Intermediate Nodes;161
10.8.3;6.8.3 Characterizing Networks Where Hub Nodes Are Significant;161
10.9;6.9 Data Analysis Implications of the Geometric Interpretation;162
10.10;6.10 Brain Cancer Network Application;164
10.11;6.11 Module and Hub Significance in Men, Mice, and Yeast;168
10.12;6.12 Summary;171
10.13;6.13 R Code for Simulating Gene Expression Data;174
10.14;6.14 Exercises;178
10.15;References;180
11;Chapter 7: Constructing Networks from Matrices;182
11.1;7.1 Turning a Similarity Matrix into a Network;182
11.2;7.2 Turning a Symmetric Matrix into a Network;183
11.3;7.3 Turning a General Square Matrix into a Network;184
11.4;7.4 Turning a Dissimilarity or Distance into a Network;185
11.5;7.5 Networks Based on Distances Between Vectors;186
11.6;7.6 Correlation Networks as Distance-Based Networks;187
11.7;7.7 Sample Networks for Outlier Detection;188
11.8;7.8 KL Dissimilarity Between Positive Definite Matrices;190
11.9;7.9 KL Pre-Dissimilarity for Parameter Estimation;191
11.10;7.10 Adjacency Function Based on Distance Properties;192
11.11;7.11 Constructing Networks from Multiple Similarity Matrices;193
11.11.1;7.11.1 Consensus and Preservation Networks;194
11.12;7.12 Exercises;196
11.13;References;199
12;Chapter 8: Clustering Procedures and Module Detection;200
12.1;8.1 Cluster Object Scatters Versus Network Densities;200
12.2;8.2 Partitioning-Around-Medoids Clustering;202
12.3;8.3 k-Means Clustering;203
12.4;8.4 Hierarchical Clustering;205
12.5;8.5 Cophenetic Distance Based on a Hierarchical Cluster Tree;207
12.6;8.6 Defining Clusters from a Hierarchical Cluster Tree: The Dynamictreecut Library for R;209
12.7;8.7 Cluster Quality Statistics Based on Network Concepts;213
12.8;8.8 Cross-Tabulation-Based Cluster (Module) Preservation Statistics;214
12.9;8.9 Rand Index and Similarity Measures Between Two Clusterings;216
12.9.1;8.9.1 Co-Clustering Formulation of the Rand Index ;217
12.9.2;8.9.2 R Code for Cross-Tabulation and Co-Clustering;218
12.10;8.10 Discussion of Clustering Methods;219
12.11;8.11 Exercises;221
12.12;References;226
13;Chapter 9: Evaluating Whether a Module is Preserved in Another Network;228
13.1;9.1 Introduction;228
13.2;9.2 Module Preservation Statistics;230
13.2.1;9.2.1 Summarizing Preservation Statistics and Threshold Values;233
13.2.2;9.2.2 Module Preservation Statistics for General Networks;234
13.2.3;9.2.3 Module Preservation Statistics for Correlation Networks;235
13.2.3.1;9.2.3.1 Eigennode-Based Density Preservation Statistics;236
13.2.3.2;9.2.3.2 Eigennode-Based Connectivity Preservation Statistics;237
13.2.3.3;9.2.3.3 Module Separability Statistics;238
13.2.4;9.2.4 Assessing Significance of Observed Module Preservation Statistics by Permutation Tests;239
13.2.5;9.2.5 Composite Preservation Statistic Zsummary;239
13.2.5.1;9.2.5.1 Thresholds for Module Preservation Statistics;240
13.2.6;9.2.6 Composite Preservation Statistic medianRank;241
13.2.6.1;9.2.6.1 Composite Preservation Statistic ZsummaryADJ for General Networks;241
13.3;9.3 Cholesterol Biosynthesis Module Between Mouse Tissues;242
13.4;9.4 Human Brain Module Preservation in Chimpanzees;245
13.5;9.5 KEGG Pathways Between Human and Chimpanzee Brains;252
13.6;9.6 Simulation Studies of Module Preservation;254
13.7;9.7 Relationships Among Module Preservation Statistics;260
13.8;9.8 Discussion of Module Preservation Statistics;263
13.9;9.9 R Code for Studying the Preservation of Modules;265
13.10;9.10 Exercises;266
13.11;References;266
14;Chapter 10: Association Measures and Statistical Significance Measures;269
14.1;10.1 Different Types of Random Variables;269
14.2;10.2 Permutation Tests for Calculating p Values;270
14.3;10.3 Computing p Values for Correlations;272
14.4;10.4 R Code for Calculating Correlation Test p Values;274
14.5;10.5 Multiple Comparison Correction Procedures for p Values;275
14.6;10.6 False Discovery Rates and q-values;278
14.7;10.7 R Code for Calculating q-values;280
14.8;10.8 Multiple Comparison Correction as p Value Transformation;282
14.9;10.9 Alternative Approaches for Dealing with Many p Values;285
14.10;10.10 R Code for Standard Screening;286
14.11;10.11 When Are Two Variable Screening Methods Equivalent?;287
14.12;10.12 Threshold-Equivalence of Linear Significance Measures;289
14.13;10.13 Network Screening;291
14.14;10.14 General Definition of an Association Network;292
14.15;10.15 Rank-Equivalence and Threshold-Equivalence;292
14.16;10.16 Threshold-Equivalence of Linear Association Networks;293
14.17;10.17 Statistical Criteria for Choosing the Threshold ;294
14.18;10.18 Exercises;294
14.19;References;297
15;Chapter 11: Structural Equation Models and Directed Networks;298
15.1;11.1 Testing Causal Models Using Likelihood Ratio Tests;298
15.1.1;11.1.1 Depicting Causal Relationships in a Path Diagram;299
15.1.2;11.1.2 Path Diagram as Set of Structural Equations;301
15.1.3;11.1.3 Deriving Model-Based Predictions of Covariances;302
15.1.4;11.1.4 Maximum Likelihood Estimates of Model Parameters;304
15.1.5;11.1.5 Model Fitting p Value and Likelihood Ratio Tests;306
15.1.6;11.1.6 Model Fitting Chi-Square Statistics and LRT;306
15.2;11.2 R Code for Evaluating an SEM Model;308
15.3;11.3 Using Causal Anchors for Edge Orienting;313
15.3.1;11.3.1 Single Anchor Local Edge Orienting Score;314
15.3.2;11.3.2 Multi-Anchor LEO Score;316
15.3.3;11.3.3 Thresholds for Local Edge Orienting Scores;318
15.4;11.4 Weighted Directed Networks Based on LEO Scores;318
15.5;11.5 Systems Genetic Applications;319
15.6;11.6 The Network Edge Orienting Method;320
15.6.1;11.6.1 Step 1: Combine Quantitative Traits and SNPs;320
15.6.2;11.6.2 Step 2: Genetic Marker Selection and Assignment to Traits;322
15.6.2.1;11.6.2.1 Manual SNP Selection;322
15.6.2.2;11.6.2.2 Automatic SNP Selection;323
15.6.3;11.6.3 Step 3: Compute Local Edge Orienting Scores for Aggregating the Genetic Evidence in Favor of a Causal Orientation;324
15.6.4;11.6.4 Step 4: For Each Edge, Evaluate the Fit of the Underlying Local SEM Models;324
15.6.5;11.6.5 Step 5: Robustness Analysis with Respect to SNP Selection Parameters;324
15.6.6;11.6.6 Step 6: Repeat the Analysis for the Next A–B Trait–Trait Edge and Apply Edge Score Thresholds to Orient the Network;326
15.6.7;11.6.7 NEO Software and Output;326
15.6.8;11.6.8 Screening for Genes that Are Reactive to Insig1 ;327
15.6.9;11.6.9 Discussion of NEO;327
15.7;11.7 Correlation Tests of Causal Models;329
15.8;11.8 R Code for LEO Scores;330
15.8.1;11.8.1 R Code for the LEO.SingleAnchor Score;330
15.8.2;11.8.2 R Code for the LEO.CPA;332
15.8.3;11.8.3 R Code for the LEO.OCA Score;334
15.9;11.9 Exercises;336
15.10;References;337
16;Chapter 12: Integrated Weighted Correlation Network Analysis of Mouse Liver Gene Expression Data;340
16.1;12.1 Constructing a Sample Network for Outlier Detection;340
16.2;12.2 Co-Expression Modules in Female Mouse Livers;343
16.2.1;12.2.1 Choosing the Soft Threshold Via Scale-Free Topology;343
16.2.2;12.2.2 Automatic Module Detection Via Dynamic Tree Cutting;345
16.2.3;12.2.3 Blockwise Module Detection for Large Networks;346
16.2.4;12.2.4 Manual, Stepwise Module Detection;347
16.2.5;12.2.5 Relating Modules to Physiological Traits;349
16.2.6;12.2.6 Output File for Gene Ontology Analysis;352
16.3;12.3 Systems Genetic Analysis with NEO;353
16.4;12.4 Visualizing the Network;356
16.4.1;12.4.1 Connectivity, TOM, and MDS Plots;356
16.4.2;12.4.2 VisANT Plot and Software;358
16.4.3;12.4.3 Cytoscape and Pajek Software;358
16.5;12.5 Module Preservation Between Female and Male Mice;359
16.6;12.6 Consensus modules Between Female and Male Liver Tissues;363
16.6.1;12.6.1 Relating Consensus Modules to the Traits;364
16.6.2;12.6.2 Manual Consensus Module Analysis;367
16.7;12.7 Exercises;369
16.8;References;370
17;Chapter 13: Networks Based on Regression Models and Prediction Methods;371
17.1;13.1 Least Squares Regression and MLE;371
17.2;13.2 R Commands for Simple Linear Regression;373
17.3;13.3 Likelihood Ratio Test for Linear Model Fit;374
17.4;13.4 Polynomial and Spline Regression Models;376
17.5;13.5 R Commands for Polynomial Regression and Spline Regression;378
17.6;13.6 Conditioning on Additional Covariates;381
17.7;13.7 Generalized Linear Models;382
17.8;13.8 Model Fitting Indices and Accuracy Measures;383
17.9;13.9 Networks Based on Predictors and Linear Models;383
17.10;13.10 Partial Correlations and Related Networks;384
17.11;13.11 R Code for Partial Correlations;386
17.12;13.12 Exercises;386
17.13;References;390
18;Chapter 14: Networks Between Categorical or Discretized Numeric Variables;391
18.1;14.1 Categorical Variables and Statistical Independence;391
18.2;14.2 Entropy;393
18.2.1;14.2.1 Estimating the Density of a Random Variable;394
18.2.2;14.2.2 Entropy of a Discretized Continuous Variable;396
18.3;14.3 Association Measures Between Categorical Vectors;397
18.3.1;14.3.1 Association Measures Expressed in Terms of Counts;399
18.3.2;14.3.2 R Code for Relating Categorical Variables;399
18.3.3;14.3.3 Chi-Square Statistic Versus Cor in Case of Binary Variables;400
18.3.4;14.3.4 Conditional Mutual Information;401
18.4;14.4 Relationships Between Networks of Categorical Vectors;402
18.5;14.5 Networks Based on Mutual Information;403
18.6;14.6 Relationship Between Mutual Information and Correlation;405
18.6.1;14.6.1 Applications for Relating MI with Cor;408
18.7;14.7 ARACNE Algorithm;409
18.7.1;14.7.1 Generalizing the ARACNE Algorithm;411
18.7.2;14.7.2 Discussion of Mutual Information Networks;412
18.7.3;14.7.3 R Packages for Computing Mutual Information;413
18.8;14.8 Exercises;414
18.9;References;417
19;Chapter 15: Network Based on the Joint Probability Distribution of Random Variables;419
19.1;15.1 Association Measures Based on Probability Densities;419
19.1.1;15.1.1 Entropy(X) Versus Entropy(Discretize(X));421
19.1.2;15.1.2 Kullback–Leibler Divergence for Assessing Model Fit;423
19.1.3;15.1.3 KL Divergence of Multivariate Normal Distributions;424
19.1.4;15.1.4 KL Divergence for Estimating Network Parameters;425
19.2;15.2 Partitioning Function for the Joint Probability;426
19.3;15.3 Discussion;427
19.4;References;428
20;Index;430