Weighted correlation network analysis, also known as weighted gene co-expression network analysis (WGCNA), is a widely used data mining method especially for studying biological networks based on pairwise correlations between variables. While it can be applied to most high-dimensional data sets, it has been most widely used in genomic applications. It allows one to define modules (clusters), intramodular hubs, and network nodes with regard to module membership, to study the relationships between co-expression modules, and to compare the network topology of different networks (differential network analysis). WGCNA can be used as a data reduction technique (related to oblique factor analysis), as a clustering method (fuzzy clustering), as a feature selection method (e.g. as gene screening method), as a framework for integrating complementary (genomic) data (based on weighted correlations between quantitative variables), and as a data exploratory technique. Although WGCNA incorporates traditional data exploratory techniques, its intuitive network language and analysis framework transcend any standard analysis technique. Since it uses network methodology and is well suited for integrating complementary genomic data sets, it can be interpreted as systems biologic or systems genetic data analysis method. By selecting intramodular hubs in consensus modules, WGCNA also gives rise to network based meta analysis techniques.
History The WGCNA method was developed by Steve Horvath, a professor of human genetics at the David Geffen School of Medicine at UCLA and of biostatistics at the UCLA Fielding School of Public Health and his colleagues at UCLA, and (former) lab members (in particular Peter Langfelder, Bin Zhang, Jun Dong). Much of the work arose from collaborations with applied researchers. In particular, weighted correlation networks were developed in joint discussions with cancer researchers Paul Mischel, Stanley F. Nelson, and neuroscientists Daniel H. Geschwind, Michael C. Oldham, according to the acknowledgement section in.
Comparison between weighted and unweighted correlation networks A weighted correlation network can be interpreted as special case of a weighted network, dependency network or correlation network. Weighted correlation network analysis can be attractive for the following reasons:
The network construction (based on soft thresholding the correlation coefficient) preserves the continuous nature of the underlying correlation information. For example, weighted correlation networks that are constructed on the basis of correlations between numeric variables do not require the choice of a hard threshold. Dichotomizing information and (hard)-thresholding may lead to information loss. The network construction gives highly robust results with respect to different choices of the soft threshold. In contrast, results based on unweighted networks, constructed by thresholding a pairwise association measure, often strongly depend on the threshold. Weighted correlation networks facilitate a geometric interpretation based on the angular interpretation of the correlation, chapter 6 in. Resulting network statistics can be used to enhance standard data-mining methods such as cluster analysis since (dis)-similarity measures can often be transformed into weighted networks; see chapter 6 in. WGCNA provides powerful module preservation statistics which can be used to quantify similarity to another condition. Also module preservation statistics allow one to study differences between the modular structure of networks. Weighted networks and correlation networks can often be approximated by "factorizable" networks. Such approximations are often difficult to achieve for sparse, unweighted networks. Therefore, weighted (correlation) networks allow for a parsimonious parametrization (in terms of modules and module membership) (chapters 2, 6 in ) and.
Method First, one defines a gene co-expression similarity measure which is used to define the network. We denote the gene co-expression similarity measure of a pair of genes i and j by s i j {\displaystyle s_{ij}} . Many co-expression studies use the absolute value of the correlation as an unsigned co-expression similarity measure,
s i j u n s i g n e d = | c o r ( x i , x j ) | {\displaystyle s_{ij}^{unsigned}=|cor(x_{i},x_{j})|}
where gene expression profiles x i {\displaystyle x_{i}} and x j {\displaystyle x_{j}} consist of the expression of genes i and j across multiple samples. However, using the absolute value of the correlation may obfuscate biologically relevant information, since no distinction is made between gene repression and activation. In contrast, in signed networks the similarity between genes reflects the sign of the correlation of their expression profiles. Varied transformation (or scaling) approaches can be considered if a signed co-expression measure between gene expression profiles x i {\displaystyle x_{i}} and x j {\displaystyle x_{j}} is needed. For example, one can (linearly) scale the correlations to be within the [ 0 , 1 ] {\displaystyle [0,1]} range by performing a simple transformation of the correlations as follows:
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