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<p>Analyzing dynamic structures in large-scale time-series data is a critical but computationally demanding task. The Compact Dual Singular Value Decomposition (CDSVD) is a powerful method for this analysis, but its high computational cost makes it difficult to scale to large datasets. To address this limitation, we propose a randomized CDSVD (RCDSVD) algorithm featuring a “Standard Part Sampling" strategy, which constructs the subspace using only the standard part. This strategy removes the computational bottleneck from expensive dual matrix multiplications (which have 3x the flops cost of standard multiplications), significantly reducing the computational load. Experiments on time-series data (such as fMRI and video) demonstrate that the RCDSVD achieves significant speedups while preserving nearly identical analytical fidelity to the CDSVD.</p>

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Randomized Compact Dual SVD and its Applications to Time-Series Analysis

  • 期刊论文

  • 发表日期：

    2026年5月29日

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  • Tong Wei,
  • Linfeng He,
  • Yimin Wei

摘要

Analyzing dynamic structures in large-scale time-series data is a critical but computationally demanding task. The Compact Dual Singular Value Decomposition (CDSVD) is a powerful method for this analysis, but its high computational cost makes it difficult to scale to large datasets. To address this limitation, we propose a randomized CDSVD (RCDSVD) algorithm featuring a “Standard Part Sampling" strategy, which constructs the subspace using only the standard part. This strategy removes the computational bottleneck from expensive dual matrix multiplications (which have 3x the flops cost of standard multiplications), significantly reducing the computational load. Experiments on time-series data (such as fMRI and video) demonstrate that the RCDSVD achieves significant speedups while preserving nearly identical analytical fidelity to the CDSVD.