Clustering gene expression data by exploiting phase transitions in granular ferromagnets requires transforming the data to a granular substrate. We present a method using the recently introduced homogeneity order parameter $\Lambda$ [H. Agrawal, Phys. Rev. Lett. 89, 268702 (2002)] for optimizing the parameter controlling the “granularity” and thus the stability of partitions. The model substrates obtained for gene expression data have a highly granular structure. We explore properties of phase transition in high $q$ ferromagnetic Potts models on these substrates and show that the maximum of the width of superparamagnetic domain, corresponding to maximally stable partitions, coincides with the minimum of $\Lambda$.

• Received 2 December 2002

DOI:https://doi.org/10.1103/PhysRevLett.90.158102