A Fixed Parameter Tractable Integer Program for Finding the Maximum Order Preserving Submatrix

International audienceOrder-preserving submatrices are an important tool for the analysis of gene expression data. As finding large order-preserving submatrices is a computationally hard problem, previous work has investigated both exact but exponential-time as well as polynomial-time but inexact algorithms for finding large order-preserving submatrices. In this paper, we propose a novel exact algorithm to find maximum order preserving submatrices which is fixed parameter tractable with respect to the number of columns of the provided gene expression data. In particular, our algorithm is based on solving a sequence of mixed integer linear programs and it exhibits better guarantees as well as better runtime performance as compared to the state-of-the-art exact algorithms. Our empirical study in benchmark datasets shows large improvement in terms of computational speed

Discovering significant relaxed order-preserving submatrices

Mining order-preserving submatrix (OPSM) patterns has received much attention from researchers, since in many scientific applications, such as those involving gene expression data, it is natural to express the data in a matrix and also important to find the order-preserving submatrix patterns. However, most current work assumes the noise-free OPSM model and thus is not practical in many real situations when sample contamination exists. In this paper, we propose a relaxed OPSM model called ROPSM. The ROPSM model supports mining more reasonable noise-corrupted OPSM patterns than another well-known model called AOPC (approximate order-preserving cluster). While OPSM mining is known to be an NP-hard problem, mining ROPSM patterns is even a harder problem. We propose a novel method called ROPSM-Growth to mine ROPSM patterns. Specifically, two pattern growing strategies, such as column-centric strategy and row-centric strategy, are presented, which are effective to grow the seed OPSMs into significant ROPSMs. An effective median-rank based method is also developed to discover the underlying true order of conditions involved in an ROPSM pattern. Our experiments on a biological dataset show that the ROPSM model better captures the characteristics of noise in gene expression data matrix compared to the AOPC model. Importantly, we find that our approach is able to detect more quality biologically significant patterns with comparable efficiency with the counterparts of AOPC. Specifically, at least 26.6% (75 out of 282) of the patterns mined by our approach are strongly associated with more than 10 gene categories (high biological significance), which is 3 times better than that obtained from using the AOPC approach. © 2010 ACM