Algorithm for low-variance biclusters to identify coregulation modules in sequencing datasets

Abstract

High-throughput sequencing (CHIP-Seq) data exhibit binding events with possible binding locations and their strengths, followed by interpretations of the locations of peaks. Recent methods tend to summarize all CHIP-Seq peaks detected within a limited up and down region of each gene into one real-valued score in order to quantify the probability of regulation in a region. Applying subspace clustering (or biclustering) techniques on these scores would discover important knowledge such as the potential co-regulation or co-factors mechanisms. The ideal biclusters generated should contain subsets of genes, and transcription factors (TF) such that the cell-values in biclusters are distributed around a mean value with low variance. Such biclusters would indicate TF sets regulating gene sets with the same probability values. However, most existing biclustering algorithms are neither able to enforce variance as a strict limitation on the values contained in a bicluster, nor use variance as the guiding metric while searching for the desirable biclusters. An algorithm that uses search spaces defined by lattices containing all overlapping biclusters and a bound on variance values as the guiding metric is presented in this paper. The algorithm is shown to be an efficient and effective method for discovering the possibly overlapping biclusters under pre-defined variance bounds. We present in this paper our algorithm, its results with synthetic and CHIP-Seq and motif datasets, and compare them with the results obtained by other algorithms to demonstrate the power and effectiveness of our algorithm.

A Biclustering Algorithm to Discover Functional Modules from ENCODE ChIP-Seq Data

“…Such co-factor modules can be defined as biclusters of low-variances [11]. The Lattice lowvariance biclustering algorithm defines an interesting bicluster to be a submatrix where (i) the number of rows is equal to or greater than a user-specified threshold; (ii) the number of columns is equal to or greater than a userspecified threshold and (iii) the standard deviation of the submatrix is equal to or less than a user-specified threshold.…”

“…The authors further prove that by restricting the Range on both rows and columns independently, the variance of the bicluster gets bounded. Since the range of a row or a column is a strictly monotonic metric, it is used as a heuristic in the search for biclusters whose variance is bounded from above [11].…”

“…Equation (3) is a useful statement as it conveys the idea that by limiting the Range of a set of values [11], their variance and standard deviation also get bounded.…”