Genomic Signal Processing

by Shmulevich, Ilya

• ISBN13: 9780691117621
• ISBN10: 0691117624
• Format: Hardcover
• Copyright: 2007-07-02
• Publisher: Princeton Univ Pr

Summary

Genomic signal processing (GSP) can be defined as the analysis, processing, and use of genomic signals to gain biological knowledge, and the translation of that knowledge into systems-based applications that can be used to diagnose and treat genetic diseases. Situated at the crossroads of engineering, biology, mathematics, statistics, and computer science, GSP requires the development of both nonlinear dynamical models that adequately represent genomic regulation, and diagnostic and therapeutic tools based on these models. This book facilitates these developments by providing rigorous mathematical definitions and propositions for the main elements of GSP and by paying attention to the validity of models relative to the data. Ilya Shmulevich and Edward Dougherty cover real-world situations and explain their mathematical modeling in relation to systems biology and systems medicine. Genomic Signal Processingmakes a major contribution to computational biology, systems biology, and translational genomics by providing a self-contained explanation of the fundamental mathematical issues facing researchers in four areas: classification, clustering, network modeling, and network intervention.

Author Biography

Ilya Shmulevich, an associate professor at the Institute for Systems Biology, is the coauthor of "Microarray Quality Control" and the coeditor of "Computational and Statistical Approaches to Genomics". Edward R. Dougherty is professor of electrical and computer engineering and director of the Genomic Signal Processing Laboratory at Texas A&M University, and director of the Computational Biology Division at the Translational Genomics Research Institute. His thirteen previous books include "Random Processes for Image and Signal Processing".

Table of Contents

Preface	p. ix
Biological Foundations
Genetics	p. 1
Nucleic Acid Structure	p. 2
Genes	p. 5
RNA	p. 6
Transcription	p. 6
Proteins	p. 9
Translation	p. 10
Transcriptional Regulation	p. 12
Genomics	p. 16
Microarray Technology	p. 17
Proteomics	p. 20
Bibliography	p. 22
Deterministic Models of Gene Networks
Graph Models	p. 23
Boolean Networks	p. 30
Cell Differentiation and Cellular Functional States	p. 33
Network Properties and Dynamics	p. 35
Network Inference	p. 49
Generalizations of Boolean Networks	p. 53
Asynchrony	p. 53
Multivalued Networks	p. 56
Differential Equation Models	p. 59
A Differential Equation Model Incorporating Transcription and Translation	p. 62
Discretization of the Continuous Differential Equation Model	p. 65
Bibliography	p. 70
Stochastic Models of Gene Networks
Bayesian Networks	p. 77
Probabilistic Boolean Networks	p. 83
Definitions	p. 86
Inference	p. 97
Dynamics of PBNs	p. 99
Steady-State Analysis of Instantaneously Random PBNs	p. 113
Relationships of PBNs to Bayesian Networks	p. 119
Growing Subnetworks from Seed Genes	p. 125
Intervention	p. 129
Gene Intervention	p. 130
Structural Intervention	p. 140
External Control	p. 145
Bibliography	p. 151
Classification
Bayes Classifier	p. 160
Classification Rules	p. 162
Consistent Classifier Design	p. 162
Examples of Classification Rules	p. 166
Constrained Classifiers	p. 168
Shatter Coefficient	p. 171
VC Dimension	p. 173
Linear Classification	p. 176
Rosenblatt Perceptron	p. 177
Linear and Quadratic Discriminant Analysis	p. 178
Linear Discriminants Based on Least-Squares Error	p. 180
Support Vector Machines	p. 183
Representation of Design Error for Linear Discriminant Analysis	p. 186
Distribution of the QDA Sample-Based Discriminant	p. 187
Neural Networks Classifiers	p. 189
Classification Trees	p. 192
Classification and Regression Trees	p. 193
Strongly Consistent Rules for Data-Dependent Partitioning	p. 194
Error Estimation	p. 196
Resubstitution	p. 196
Cross-validation	p. 198
Bootstrap	p. 199
Bolstering	p. 201
Error Estimator Performance	p. 204
Feature Set Ranking	p. 207
Error Correction	p. 209
Robust Classifiers	p. 213
Optimal Robust Classifiers	p. 214
Performance Comparison for Robust Classifiers	p. 216
Bibliography	p. 221
Regularization
Data Regularization	p. 225
Regularized Discriminant Analysis	p. 225
Noise Injection	p. 228
Complexity Regularization	p. 231
Regularization of the Error	p. 231
Structural Risk Minimization	p. 233
Empirical Complexity	p. 236
Feature Selection	p. 237
Peaking Phenomenon	p. 237
Feature Selection Algorithms	p. 243
Impact of Error Estimation on Feature Selection	p. 244
Redundancy	p. 245
Parallel Incremental Feature Selection	p. 249
Bayesian Variable Selection	p. 251
Feature Extraction	p. 254
Bibliography	p. 259
Clustering
Examples of Clustering Algorithms	p. 263
Euclidean Distance Clustering	p. 264
Self-Organizing Maps	p. 265
Hierarchical Clustering	p. 266
Model-Based Cluster Operators	p. 268
Cluster Operators	p. 269
Algorithm Structure	p. 269
Label Operators	p. 271
Bayes Clusterer	p. 273
Distributional Testing of Cluster Operators	p. 274
Cluster Validation	p. 276
External Validation	p. 276
Internal Validation	p. 277
Instability Index	p. 278
Bayes Factor	p. 280
Learning Cluster Operators	p. 281
Empirical-Error Cluster Operator	p. 281
Nearest-Neighbor Clustering Rule	p. 283
Bibliography	p. 292
Index	p. 295
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