Correlation networks are increasingly being used in bioinformatics applications For example, weighted gene co-expression network analysis is a systems biology method for describing the correlation patterns among genes across microarray samples Weighted correlation network analysis (WGCNA) can be used for finding clusters (modules) of highly correlated genes, for summarizing such clusters using the module eigengene or an intramodular hub gene, for relating modules to one another and to external sample traits (using eigengene network methodology), and for calculating module membership measures Correlation networks facilitate network based gene screening methods that can be used to identify candidate biomarkers or therapeutic targets These methods have been successfully applied in various biological contexts, eg cancer, mouse genetics, yeast genetics, and analysis of brain imaging data While parts of the correlation network methodology have been described in separate publications, there is a need to provide a user-friendly, comprehensive, and consistent software implementation and an accompanying tutorial The WGCNA R software package is a comprehensive collection of R functions for performing various aspects of weighted correlation network analysis The package includes functions for network construction, module detection, gene selection, calculations of topological properties, data simulation, visualization, and interfacing with external software Along with the R package we also present R software tutorials While the methods development was motivated by gene expression data, the underlying data mining approach can be applied to a variety of different settings The WGCNA package provides R functions for weighted correlation network analysis, eg co-expression network analysis of gene expression data The R package along with its source code and additional material are freely available at http://wwwgeneticsuclaedu/labs/horvath/CoexpressionNetwork/Rpackages/WGCNA
 

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WGCNA: an R package for weighted correlation network analysis.

Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

Proteins and their functional interactions form the backbone of the cellular machinery. Their connectivity network needs to be considered for the full understanding of biological phenomena, but the available information on protein-protein associations is incomplete and exhibits varying levels of annotation granularity and reliability. The STRING database aims to collect, score and integrate all publicly available sources of protein-protein interaction information, and to complement these with computational predictions. Its goal is to achieve a comprehensive and objective global network, including direct (physical) as well as indirect (functional) interactions. The latest version of STRING (11.0) more than doubles the number of organisms it covers, to 5090. The most important new feature is an option to upload entire, genome-wide datasets as input, allowing users to visualize subsets as interaction networks and to perform gene-set enrichment analysis on the entire input. For the enrichment analysis, STRING implements well-known classification systems such as Gene Ontology and KEGG, but also offers additional, new classification systems based on high-throughput text-mining as well as on a hierarchical clustering of the association network itself. The STRING resource is available online at https://string-db.org/.

https://www.zora.uzh.ch/id/eprint/165500/1/30476243.pdf

STRING v11: protein-protein association networks with increased coverage, supporting functional discovery in genome-wide experimental datasets.

Comprehensive Integration of Single-Cell Data.

We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

Summary: Hierarchical clustering is a widely used method for detecting clusters in genomic data. Clusters are defined by cutting branches off the dendrogram. A common but inflexible method uses a constant height cutoff value; this method exhibits suboptimal performance on complicated dendrograms. We present the Dynamic Tree Cut R package that implements novel dynamic branch cutting methods for detecting clusters in a dendrogram depending on their shape. Compared to the constant height cutoff method, our techniques offer the following advantages: (1) they are capable of identifying nested clusters; (2) they are flexible—cluster shape parameters can be tuned to suit the application at hand; (3) they are suitable for automation; and (4) they can optionally combine the advantages of hierarchical clustering and partitioning around medoids, giving better detection of outliers. We illustrate the use of these methods by applying them to protein–protein interaction network data and to a simulated gene expression data set.

Availability: The Dynamic Tree Cut method is implemented in an R package available at http://www.genetics.ucla.edu/labs/horvath/CoexpressionNetwork/BranchCutting

Contact: stevitihit@yahoo.com

Supplementary information: Supplementary data are available at Bioinformatics online.

Defining clusters from a hierarchical cluster tree

Many high-throughput biological data analyses require the calculation of large correlation matrices and/or clustering of a large number of objects. The standard R function for calculating Pearson correlation can handle calculations without missing values efficiently, but is inefficient when applied to data sets with a relatively small number of missing data. We present an implementation of Pearson correlation calculation that can lead to substantial speedup on data with relatively small number of missing entries. Further, we parallelize all calculations and thus achieve further speedup on systems where parallel processing is available. A robust correlation measure, the biweight midcorrelation, is implemented in a similar manner and provides comparable speed. The functions cor and bicor for fast Pearson and biweight midcorrelation, respectively, are part of the updated, freely available R package WGCNA.The hierarchical clustering algorithm implemented in R function hclust is an order n(3) (n is the number of clustered objects) version of a publicly available clustering algorithm (Murtagh 2012). We present the package flashClust that implements the original algorithm which in practice achieves order approximately n(2), leading to substantial time savings when clustering large data sets.

https://www.jstatsoft.org/article/view/v046i11/v46i11.pdf

Fast R Functions for Robust Correlations and Hierarchical Clustering

In many applications, one is interested in determining which of the properties of a network module change across conditions. For example, to validate the existence of a module, it is desirable to show that it is reproducible (or preserved) in an independent test network. Here we study several types of network preservation statistics that do not require a module assignment in the test network. We distinguish network preservation statistics by the type of the underlying network. Some preservation statistics are defined for a general network (defined by an adjacency matrix) while others are only defined for a correlation network (constructed on the basis of pairwise correlations between numeric variables). Our applications show that the correlation structure facilitates the definition of particularly powerful module preservation statistics. We illustrate that evaluating module preservation is in general different from evaluating cluster preservation. We find that it is advantageous to aggregate multiple preservation statistics into summary preservation statistics. We illustrate the use of these methods in six gene co-expression network applications including 1) preservation of cholesterol biosynthesis pathway in mouse tissues, 2) comparison of human and chimpanzee brain networks, 3) preservation of selected KEGG pathways between human and chimpanzee brain networks, 4) sex differences in human cortical networks, 5) sex differences in mouse liver networks. While we find no evidence for sex specific modules in human cortical networks, we find that several human cortical modules are less preserved in chimpanzees. In particular, apoptosis genes are differentially co-expressed between humans and chimpanzees. Our simulation studies and applications show that module preservation statistics are useful for studying differences between the modular structure of networks. Data, R software and accompanying tutorials can be downloaded from the following webpage: http://www.genetics.ucla.edu/labs/horvath/CoexpressionNetwork/ModulePreservation.

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Is my network module preserved and reproducible

There is evidence that genes and their protein products are organized into functional modules according to cellular processes and pathways. Gene co-expression networks have been used to describe the relationships between gene transcripts. Ample literature exists on how to detect biologically meaningful modules in networks but there is a need for methods that allow one to study the relationships between modules. We show that network methods can also be used to describe the relationships between co-expression modules and present the following methodology. First, we describe several methods for detecting modules that are shared by two or more networks (referred to as consensus modules). We represent the gene expression profiles of each module by an eigengene. Second, we propose a method for constructing an eigengene network, where the edges are undirected but maintain information on the sign of the co-expression information. Third, we propose methods for differential eigengene network analysis that allow one to assess the preservation of network properties across different data sets. We illustrate the value of eigengene networks in studying the relationships between consensus modules in human and chimpanzee brains; the relationships between consensus modules in brain, muscle, liver, and adipose mouse tissues; and the relationships between male-female mouse consensus modules and clinical traits. In some applications, we find that module eigengenes can be organized into higher level clusters which we refer to as meta-modules. Eigengene networks can be effective and biologically meaningful tools for studying the relationships between modules of a gene co-expression network. The proposed methods may reveal a higher order organization of the transcriptome. R software tutorials, the data, and supplementary material can be found at the following webpage: http://www.genetics.ucla.edu/labs/horvath/CoexpressionNetwork/EigengeneNetwork
 .

/pdf/eigengene-networks-for-studying-the-relationships-between-co-4i8bs1nbj6.pdf

Peter Langfelder

Papers

WGCNA: an R package for weighted correlation network analysis.

Defining clusters from a hierarchical cluster tree

Fast R Functions for Robust Correlations and Hierarchical Clustering

Is my network module preserved and reproducible

Eigengene networks for studying the relationships between co-expression modules