Research Paper#Graph Theory, Matrix Completion, Machine Learning🔬 ResearchAnalyzed: Jan 3, 2026 16:42
Graph Constructions for Matrix Completion
Analysis
This paper explores deterministic graph constructions that enable unique and stable completion of low-rank matrices. The research connects matrix completability to specific patterns in the lattice graph derived from the bi-adjacency matrix's support. This has implications for designing graph families where exact and stable completion is achievable using the sum-of-squares hierarchy, which is significant for applications like collaborative filtering and recommendation systems.
Key Takeaways
- •Investigates deterministic graph constructions for matrix completion.
- •Relates completability to patterns in the lattice graph.
- •Enables the design of graph families for exact and stable completion.
- •Utilizes the sum-of-squares hierarchy for completion.
Reference
“The construction makes it possible to design infinite families of graphs on which exact and stable completion is possible for every fixed rank matrix through the sum-of-squares hierarchy.”