Two-stage linked component analysis for joint decomposition of multiple biologically related data sets

Abstract

Integrative analysis of multiple data sets has the potential of fully leveraging the vast amount of high throughput biological data being generated. In particular such analysis will be powerful in making inference from publicly available collections of genetic, transcriptomic and epigenetic data sets which are designed to study shared biological processes, but which vary in their target measurements, biological variation, unwanted noise, and batch variation. Thus, methods that enable the joint analysis of multiple data sets are needed to gain insights into shared biological processes that would otherwise be hidden by unwanted intra-data set variation. Here, we propose a method called two-stage linked component analysis (2s-LCA) to jointly decompose multiple biologically related experimental data sets with biological and technological relationships that can be structured into the decomposition. The consistency of the proposed method is established and its empirical performance is evaluated via simulation studies. We apply 2s-LCA to jointly analyze four data sets focused on human brain development and identify meaningful patterns of gene expression in human neurogenesis that have shared structure across these data sets.

Keywords: Integrative methods; Joint decomposition; Low rank models; Multiview data; Principal component analysis.

Fig. 1.

Comparisons between JIVE, AJIVE, BIDIFAC, SLIDE, BIDIFAC+, and 2s-LCA with known dimensions of spaces. (a) and (b) are both under the low-dimensional setting with ; (c) and (d) are under high dimensional setting with . For each setting, simulations are run.

Fig. 2.

Comparisons between SLIDE, BIDIFAC+ and 2s-LCA. (a) and (b) are both under the low-dimensional setting with ; (c) and (d) are under high dimensional setting with . For each setting, simulations are run.

Fig. 3.

(a) Scatterplots of scores corresponding to the top two principal components of each data set by separate PCA and (b) Scatterplots of scores of each data set corresponding to common components (top panel), partially shared components associated with environments (middle panel: on the left two plots and on the right two plots), and partially shared components associated with technologies (bottom panel: bulk on the left two plots and single cell on the right two plots) by the proposed 2s-LCA. The 4 columns in both parts correspond to the data sets: (1) van de Leemput: + bulk; (2) Yao: + single cell; (3) BrainSpan: + bulk; and (4) Nowakowski: + single cell. Each point corresponds to either one tissue sample or one cell and is colored by the transformed expression level of the DCX gene. Blue arrows indicate alignment of the first common component (-axis in top row of panels in (b) with DCX expression (neurogenesis) in all four data sets. Black circles indicate pluripotent stem cells, which are present only in the data sets.

Fig. 4.

This figure is a recoloring of the data shown in Figure 3, in order to show effects across time. Each point corresponds to either one tissue sample or one cell and is colored by days of neural differentiation for the data sets and age in years or gestational weeks for the data sets. Red arrows indicate alignment of the second common component (-axis in top row of panels in (b) with developmental time in all four data sets. Black circles indicate pluripotent stem cells, which are present only in the data sets.

Fig. 5.

Biological validation by projecting additional data sets onto common components obtained from 2s-LCA. (a) Projection of eight additional scRNA-seq data sets onto the common components with cells colored by the transformed expression level of the DCX gene. Blue arrows indicate alignment of the first common component with DCX expression (neurogenesis). (b) Projection of the same data sets onto the common components with cells colored by time: days of neural differentiation for the data sets and age in years or gestational weeks for the data sets. Red arrows indicate alignment of the second common component with developmental time. The Darmanis and others (2015) prenatal study did not specify the exact age of the 4 fetal tissue donors used in their prenatal study, indicating only 16–18 gestational weeks for all samples.