Matrix factorization for transcriptional regulatory network inference

Abstract

Inference of Transcriptional Regulatory Networks (TRNs) provides insight into the mechanisms driving biological systems, especially mammalian development and disease. Many techniques have been developed for TRN estimation from indirect biochemical measurements. Although successful when initially tested in model organisms, these regulatory models often fail when applied to data from multicellular organisms where multiple regulation and gene reuse increase dramatically. Non-negative matrix factorization techniques were initially introduced to find non-orthogonal patterns in data, making them ideal techniques for inference in cases of multiple regulation. We review these techniques and their application to TRN analysis.

Enter the matrix: factorization uncovers knowledge from omics Names/Affiliations

“…The computational differences between these algorithms have been described in numerous reviews (Berry et al, 2007;Devarajan, 2008;Ochs and Fertig, 2012;Wang and Zhang, 2013) . Perhaps the most prominent of methods is principal component analysis (PCA).…”

“…In the extreme case of "binary factorizations", all elements of the amplitude matrix are either zero or one and therefore require no thresholding to define gene modules (Zhang et al, 2010) . Encoding less stringent sparsity constraints has been found to further improve pathway inference because it models biological parsimony (Gao and Church, 2005;Kim and Tidor, 2003;Kossenkov andOchs, 2010, 2009;Ochs and Fertig, 2012) .…”

“…Correspondence analysis ( (Abdi and Williams, 2010;Fellenberg et al, 2001) independent component analysis (ICA), (Hyvärinen et al, 2004;Kong et al, 2008;Lee and Batzoglou, 2003;Yao et al, 2012) , factor analysis (Abdi et al, 2013;Wouters et al, 2003) , canonical correlation analysis (CCA) (Lê Cao et al, 2009;Takane et al, 2008; , Laplacian eigenmaps, and spectral maps (Wouters et al, 2003) are related to the mathematics mainstays of singular value decomposition (SVD) (Eckart and Young, 1936) , and principal component analysis (PCA) (Hotelling, 1933;Ma and Dai, 2011;Pearson, 1901;Wall et al, 2003) based analysis. While, Non-negative Matrix Factorization (NMF) (Devarajan, 2008;Ochs and Fertig, 2012) , manifold learning (Maindonald, 2009;Moon et al, 2017) , and compressed sensing (Cleary et al, 2017;Vattikuti et al, 2014) draw on image processing methods (Lee and Seung, 1999;Ochs et al, 1999) . With the rapidly accelerating rate of high-throughput biological data acquisition, these MF techniques enable expanding beyond simple single study designs to power systems-level analyses.…”

“…Plots of the weights of genes or samples in each component can be used to learn sources of separation in the data (Roden et al, 2006) . Because PCA learns features that explain most of the variation in the data, the algorithm will necessarily combine signal from the multiple sources of biological and technical factors in the data (Ochs and Fertig, 2012) . In this regard, PCA may be of use only in experimental paradigms in which the processes or conditions of interest represent the strongest sources of variation by design, and of less use as an exploratory approach in more unstructured experimental designs.…”

“…Here, we review the applications of MF algorithms to high-throughput biology and how the results of these applications are interpreted to provide new biological knowledge. There are numerous reviews discussing the mathematical and technical details of MF algorithms (Abdi et al, 2013;Li et al, 2016;Meng et al, 2016c;Ochs and Fertig, 2012) and their applications to microarray data (Devarajan, 2008) . In this review, we focus on the subject of biological applications of MF algorithms and the interpretation of their results for in silico experimentation for the first time since the advent of sequencing technologies.…”