GCM: metric-guided clustering by genetic algorithm for correlation-defined modules

Gene co-expression analyses identify "good" modules by a correlation criterion. However, standard pipelines detect modules with greedy algorithms that optimize other quantities and only measure correlation afterwards. We present a method called Genetic Clustering by Metric (GCM), an open-source Python tool that closes this gap by treating module detection as maximum-likelihood inference and solving it globally. In GCM, the correlation objective is, up to a constant and the sample-size factor, the profile log-likelihood of an explicit generative model: a block-diagonal one-factor Gaussian in which each module is a single regulator with equal-magnitude loadings. This bases model selection on a principled footing through a genuine BIC/AIC in correlation space. GCM maximizes this likelihood with a memetic genetic algorithm: a population-based search hybridized with a greedy local refinement that reassigns genes after the fact, a move the agglomerative clustering at the core of co-expression pipelines cannot make. Across a replicated noise sweep, GCM reproducibly surpasses hierarchical correlation clustering and k-means with the lowest variance, and an ablation shows the local-search step is responsible; the advantage persists when the number of modules is unknown and when unstructured genes must be ignored. GCM faithfully optimizes geometric indices on the Iris benchmark dataset. For a breast-cancer RNA-seq it recovers coherent modules that predict tumor-versus-normal status.GCM depends only on NumPy and SciPy and exposes one swappable-metric interface with single- and multi-objective modes.