D-SLR: The Disjoint Row-Sparse plus Low-Rank Decomposition
We propose the Disjoint Row-Sparse plus Low-Rank (D-SLR) decomposition, a closed-form drop-in for the truncated SVD that improves or exactly matches it.
ProofPaper ↗
Key points
- Compressing a matrix for reconstruction still defaults to the truncated SVD, approximating the data with a single low-rank structure.
- It is common to reduce the residual further by adding an overlapping row-sparse component, but methods that solve this joint problem often require iterative solvers and tuning of regularization parameters.
- With zero stored rows D-SLR reduces to the truncated SVD, so it never does worse at equal cost.
- We derive an assumption-free, a-posteriori lower bound on the error at every shape, giving each solution a computable certificate on the potential gain of any other choice of rank and stored rows.
Sources (1)
- [1]D-SLR: The Disjoint Row-Sparse plus Low-Rank DecompositionarXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 7, 02:07 PM
We propose the Disjoint Row-Sparse plus Low-Rank (D-SLR) decomposition, a closed-form drop-in for the truncated SVD that improves or exactly matches it.
Compressing a matrix for reconstruction still defaults to the truncated SVD, approximating the data with a single low-rank structure.
Extractive summary: sentences quoted from the sources.