Resumen de A preconditioned conjugate gradient algorithm for GeneRank with application to microarray data mining

Gang Wu, Wei Xu, Ying Zhang, Yimin Wei

• The problem of identifying key genes is of fundamental importance in biology and medicine. The GeneRank model explores connectivity data to produce a prioritization of the genes in a microarray experiment that is less susceptible to variation caused by experimental noise than the one based on expression levels alone. The GeneRank algorithm amounts to solving an unsymmetric linear system. However, when the matrix in question is very large, the GeneRank algorithm is inefficient and even can be infeasible. On the other hand, the adjacency matrix is symmetric in the GeneRank model, while the original GeneRank algorithm fails to exploit the symmetric structure of the problem in question. In this paper, we discover that the GeneRank problem can be rewritten as a symmetric positive definite linear system, and propose a preconditioned conjugate gradient algorithm to solve it. Numerical experiments support our theoretical results, and show superiority of the novel algorithm.The problem of identifying key genes is of fundamental importance in biology and medicine. The GeneRank model explores connectivity data to produce a prioritization of the genes in a microarray experiment that is less susceptible to variation caused by experimental noise than the one based on expression levels alone. The GeneRank algorithm amounts to solving an unsymmetric linear system. However, when the matrix in question is very large, the GeneRank algorithm is inefficient and even can be infeasible. On the other hand, the adjacency matrix is symmetric in the GeneRank model, while the original GeneRank algorithm fails to exploit the symmetric structure of the problem in question. In this paper, we discover that the GeneRank problem can be rewritten as a symmetric positive definite linear system, and propose a preconditioned conjugate gradient algorithm to solve it. Numerical experiments support our theoretical results, and show superiority of the novel algorithm.