Hierarchical nuclear norm penalization for multi-view data integration.

Area of Science:

• Bioinformatics
• Computational Biology
• Statistical Genetics

Background:

• Multi-view data integration is crucial for analyzing complex biological samples from diverse sources.
• Low-rank matrix factorization methods are common but struggle with partially-shared structures.
• Existing methods often have restrictive models or identifiability conditions for shared signals.

Purpose of the Study:

• To develop a new data integration method capable of modeling partially-shared structures in multi-view data.
• To introduce a novel penalty, the hierarchical nuclear norm (HNN), for improved signal estimation.
• To provide identifiable guarantees for hierarchical signal structures under specific conditions.

Main Methods:

• Proposed a new formulation for signal structures using hierarchical levels for multi-view data.
• Introduced the hierarchical nuclear norm (HNN) penalty for convex optimization.
• Utilized a dual forward-backward algorithm for solving the optimization problem.
• Developed a refitting procedure and bi-cross-validation for parameter selection.

Main Results:

• The proposed HNN penalty effectively models partially-shared structures without restrictive factorization.
• The method leads to a convex optimization problem solvable efficiently.
• Simulation studies and genotype-tissue expression data analysis show superior performance compared to existing methods.
• Demonstrated advantages in dimension reduction, exploratory analysis, and cross-view association quantification.

Conclusions:

• The novel HNN-based method offers a robust and flexible approach for multi-view data integration.
• This method overcomes limitations of existing techniques in handling partially-shared signals.
• The approach is validated through simulations and real-world biological data, showing significant improvements.