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Abstract Multi‐view data, which is matched sets of measurements on the same subjects, have become increasingly common with advances in multi‐omics technology. Often, it is of interest to find associations between the views that are related to the intrinsic class memberships. Existing association methods cannot directly incorporate class information, while existing classification methods do not take into account between‐views associations. In this work, we propose a framework for Joint Association and Classification Analysis of multi‐view data (JACA). Our goal is not to merely improve the misclassification rates, but to provide a latent representation of high‐dimensional data that is both relevant for the subtype discrimination and coherent across the views. We motivate the methodology by establishing a connection between canonical correlation analysis and discriminant analysis. We also establish the estimation consistency of JACA in high‐dimensional settings. A distinct advantage of JACA is that it can be applied to the multi‐view data with block‐missing structure, that is to cases where a subset of views or class labels is missing for some subjects. The application of JACA to quantify the associations between RNAseq and miRNA views with respect to consensus molecular subtypes in colorectal cancer data from The Cancer Genome Atlas project leads to improved misclassification rates and stronger found associations compared to existing methods.
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Hierarchical Nuclear Norm Penalization for Multi-View Data Integration
Abstract The prevalence of data collected on the same set of samples from multiple sources (i.e., multi-view data) has prompted significant development of data integration methods based on low-rank matrix factorizations. These methods decompose signal matrices from each view into the sum of shared and individual structures, which are further used for dimension reduction, exploratory analyses, and quantifying associations across views. However, existing methods have limitations in modeling partially-shared structures due to either too restrictive models, or restrictive identifiability conditions. To address these challenges, we propose a new formulation for signal structures that include partially-shared signals based on grouping the views into so-called hierarchical levels with identifiable guarantees under suitable conditions. The proposed hierarchy leads us to introduce a new penalty, hierarchical nuclear norm (HNN), for signal estimation. In contrast to existing methods, HNN penalization avoids scores and loadings factorization of the signals and leads to a convex optimization problem, which we solve using a dual forward–backward algorithm. We propose a simple refitting procedure to adjust the penalization bias and develop an adapted version of bi-cross-validation for selecting tuning parameters. Extensive simulation studies and analysis of the genotype-tissue expression data demonstrate the advantages of our method over existing alternatives.
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- PAR ID:
- 10441486
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Biometrics
- Volume:
- 79
- Issue:
- 4
- ISSN:
- 0006-341X
- Format(s):
- Medium: X Size: p. 2933-2946
- Size(s):
- p. 2933-2946
- Sponsoring Org:
- National Science Foundation
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