Principal curve approaches for inferring 3D chromatin architecture.

Three-dimensional (3D) genome spatial organization is critical for numerous cellular processes, including transcription, while certain conformation-driven structural alterations are frequently oncogenic. Genome architecture had been notoriously difficult to elucidate, but the advent of the suite of chromatin conformation capture assays, notably Hi-C, has transformed understanding of chromatin structure and provided downstream biological insights. Although many findings have flowed from direct analysis of the pairwise proximity data produced by these assays, there is added value in generating corresponding 3D reconstructions deriving from superposing genomic features on the reconstruction. Accordingly, many methods for inferring 3D architecture from proximity data have been advanced. However, none of these approaches exploit the fact that single chromosome solutions constitute a one-dimensional (1D) curve in 3D. Rather, this aspect has either been addressed by imposition of constraints, which is both computationally burdensome and cell type specific, or ignored with contiguity imposed after the fact. Here, we target finding a 1D curve by extending principal curve methodology to the metric scaling problem. We illustrate how this approach yields a sequence of candidate solutions, indexed by an underlying smoothness or degrees-of-freedom parameter, and propose methods for selection from this sequence. We apply the methodology to Hi-C data obtained on IMR90 cells and so are positioned to evaluate reconstruction accuracy by referencing orthogonal imaging data. The results indicate the utility and reproducibility of our principal curve approach in the face of underlying structural variation.

Canonical correlation analysis in high dimensions with structured regularization.

Canonical correlation analysis (CCA) is a technique for measuring the association between two multivariate data matrices. A regularized modification of canonical correlation analysis (RCCA) which imposes an ℓ2 penalty on the CCA coefficients is widely used in applications with high-dimensional data. One limitation of such regularization is that it ignores any data structure, treating all the features equally, which can be ill-suited for some applications. In this article we introduce several approaches to regularizing CCA that take the underlying data structure into account. In particular, the proposed group regularized canonical correlation analysis (GRCCA) is useful when the variables are correlated in groups. We illustrate some computational strategies to avoid excessive computations with regularized CCA in high dimensions. We demonstrate the application of these methods in our motivating application from neuroscience, as well as in a small simulation example.

Relating whole-brain functional connectivity to self-reported negative emotion in a large sample of young adults using group regularized canonical correlation analysis.

The goal of our study was to use functional connectivity to map brain function to self-reports of negative emotion. In a large dataset of healthy individuals derived from the Human Connectome Project (N = 652), first we quantified functional connectivity during a negative face-matching task to isolate patterns induced by emotional stimuli. Then, we did the same in a complementary task-free resting state condition. To identify the relationship between functional connectivity in these two conditions and self-reports of negative emotion, we introduce group regularized canonical correlation analysis (GRCCA), a novel algorithm extending canonical correlations analysis to model the shared common properties of functional connectivity within established brain networks. To minimize overfitting, we optimized the regularization parameters of GRCCA using cross-validation and tested the significance of our results in a held-out portion of the data set using permutations. GRCCA consistently outperformed plain regularized canonical correlation analysis. The only canonical correlation that generalized to the held-out test set was based on resting state data (r = 0.175, permutation test p = 0.021). This canonical correlation loaded primarily on Anger-aggression. It showed high loadings in the cingulate, orbitofrontal, superior parietal, auditory and visual cortices, as well as in the insula. Subcortically, we observed high loadings in the globus pallidus. Regarding brain networks, it loaded primarily on the primary visual, orbito-affective and ventral multimodal networks. Here, we present the first neuroimaging application of GRCCA, a novel algorithm for regularized canonical correlation analyses that takes into account grouping of the variables during the regularization scheme. Using GRCCA, we demonstrate that functional connections involving the visual, orbito-affective and multimodal networks are promising targets for investigating functional correlates of subjective anger and aggression. Crucially, our approach and findings also highlight the need of cross-validation, regularization and testing on held out data for correlational neuroimaging studies to avoid inflated effects.