eigengene

An eigengene is a concept used in gene co-expression analysis, most commonly within Weighted Gene Co-expression Network Analysis (WGCNA). It refers to the first principal component of the expression data for a module of co-expressed genes and serves as a representative expression profile for that module.

Computation wise, for a given module comprising a set of genes, one builds an expression matrix with samples as rows and the module's genes as columns. The data are typically standardized across samples (for example, z-scored). Principal component analysis is then applied to this matrix, and the first principal component—the module eigengene—is taken as a vector of length equal to the number of samples. In practice, this vector summarizes the dominant expression pattern of all genes in the module.

Module eigengenes are used to relate gene modules to external traits. By correlating an eigengene with phenotypic or clinical variables, researchers can identify modules associated with traits of interest. They also enable assessment of module membership, where each gene’s expression is correlated with the module eigengene to identify hub genes with strong module-wide influence.

Interpretation and limitations are important. The eigengene provides a single, compact representation of a module’s expression but may oversimplify complex patterns within a module. Its calculation depends on data preprocessing, normalization, and sample size, and it can be influenced by outliers. Nonetheless, eigengenes facilitate downstream analyses by reducing dimensionality and enabling straightforward module-phenotype associations.