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A Hierarchical Singular Value Decomposition Algorithm for Low Rank Matrices

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arxiv 1710.02812 v2 pith:URMHP6QZ submitted 2017-10-08 cs.NA cs.NA

Vinita Vasudevan , M. Ramakrishna This is my paper · ORCID
classification cs.NA
keywords matricestruncatedalgorithmsingularblocksdecompositionmatrixobtain
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Singular value decomposition (SVD) is a widely used technique for dimensionality reduction and computation of basis vectors. In many applications, especially in fluid mechanics and image processing the matrices are dense, but low-rank matrices. In these cases, a truncated SVD corresponding to the most significant singular values is sufficient. In this paper, we propose a tree based merge-and-truncate algorithm to obtain an approximate truncated SVD of the matrix. Unlike previous methods, our technique is not limited to "tall and skinny" or "short and fat" matrices and it can be used for matrices of arbitrary size. The matrix is partitioned into blocks and the truncated SVDs of blocks are merged to obtain the final SVD. If the matrices are low rank, this algorithm gives significant speedup over finding the truncated SVD, even when run on a single core. The error is typically less than 3\%.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. PACT: Preserving Anchored Cores in Task-vectors for Model Merging

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    PACT preserves load-bearing wall dimensions from pre-trained weights inside task vectors to reduce conflicts and improve merged model performance.

  2. Accurate and Resource-Efficient Federated Continual Learning

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    FedRAN achieves up to 4.8 pp higher accuracy in federated continual learning while using 30-122× less per-client communication by transmitting truncated-SVD summaries of random-feature Gram matrices and performing clo...

  3. No Task Left Behind: Isotropic Model Merging with Common and Task-Specific Subspaces

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    Uniformly rescaling singular values of summed task updates, plus adding task-specific residual directions, improves multi-task model merging.

  4. Learnable Similarity and Dissimilarity Guided Symmetric Non-Negative Matrix Factorization

    cs.LG 2024-12 conditional novelty 6.0 of 10

    A symmetric nonnegative matrix factorization variant that learns weights over nearest-neighbor slices for similarity and dissimilarity, plus a column-wise orthogonality regularizer, improves clustering on eight benchmarks.

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