Reconstructing the pathways of a cellular system from genome-scale signals by using matrix and tensor computations
Reconstructing the pathways of a cellular system from genome-scale signals by using matrix and tensor computations
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DOI：
10.1073/pnas.0509033102
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发表时间：
2005-12-06
影响因子：
11.1
通讯作者：
Golub, GH
中科院分区：
文献类型：
--
作者：
Alter, O;Golub, GH
我们描述了矩阵特征值分解（EVD）和伪逆投影以及张量高阶 EVD（HOEVD）在从系统基因之间的基因组规模无向相关网络重建组成细胞系统的途径中的使用。 EVD 将基因 x 基因网络制定为基因 x 基因装饰相关和解耦的 1 级子网络的线性叠加，该子网络可以与功能独立的途径相关联。从“数据”信号计算到指定“基础”信号的网络的综合伪逆投影将网络近似为仅两个信号共有的子网络的线性叠加，并模拟仅对两个实验中明显的路径的观察。我们定义了一个比较 HOEVD，它将一系列网络表示为去相关的 1 级子网络和这些子网络之间的 2 级耦合的线性叠加，这些子网络可以与独立路径以及它们之间的转换相关联，这些路径对于该系列中的所有网络来说是公共的，或者是网络子集所独有的。离散子网络和耦合的布尔函数突出了基因之间的差异（即路径依赖）关系。我们通过对酵母 DNA 微阵列数据的分析来说明基因组规模网络的 EVD、伪逆投影和 HOEVD。
We describe the use of the matrix eigenvalue decomposition (EVD) and pseudoinverse projection and a tensor higher-order EVD (HOEVD) in reconstructing the pathways that compose a cellular system from genome-scale nondirectional networks of correlations among the genes of the system. The EVD formulates a genes x genes network as a linear superposition of genes x genes decor-related and decoupled rank-1 subnetworks, which can be associated with functionally independent pathways. The integrative pseudoinverse projection of a network computed from a "data" signal onto a designated "basis" signal approximates the network as a linear superposition of only the subnetworks that are common to both signals and simulates observation of only the pathways that are manifest in both experiments. We define a comparative HOEVD that formulates a series of networks as linear superpositions of decorrelated rank-1 subnetworks and the rank-2 couplings among these subnetworks, which can be associated with independent pathways and the transitions among them common to all networks in the series or exclusive to a subset of the networks. Boolean functions of the discretized subnetworks and couplings highlight differential, i.e., pathway-dependent, relations among genes. We illustrate the EVD, pseudoinverse projection, and HOEVD of genome-scale networks with analyses of yeast DNA microarray data.