Potts ferromagnets on coexpressed gene networks: identifying maximally stable partitions.
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.
Agrawal
Himanshu
H
Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel. feagrawa@wicc.weizmann.ac.il
Domany
Eytan
E
D003110:Colonic Neoplasms / Q000235:genetics; D015870:Gene Expression; D006801:Humans; D008957:Models, Genetic; D005810:Multigene Family