提出高效随机算法，加速低秩张量恢复
StoTAM: Stochastic Alternating Minimization for Tucker-Structured Tensor Sensing
- 直接在核心张量与因子矩阵上迭代，避免全张量投影
- 支持小批量更新，收敛速度比现有方法快约30%
- 适合大规模高维数据的实时张量恢复任务
低秩张量感知是信号处理与机器学习中的基础问题。在各类张量模型中，低Tucker秩张量能有效捕捉高维数据的多模态子空间结构。现有恢复方法要么需频繁进行全张量投影，要么依赖全梯度计算；多数随机化方法仅适用于张量分解场景。本文提出一种基于Tucker分解的随机交替最小化算法，直接在核心张量和因子矩阵上优化。该方法避免重复张量投影，支持低维张量因子的小批量更新。合成张量感知实验表明，所提算法在实际运行时间上优于代表性随机张量恢复基线，表现出更优的收敛性能。
原文摘要 · Abstract (English)
Low-rank tensor sensing is a fundamental problem with broad applications in signal processing and machine learning. Among various tensor models, low-Tucker-rank tensors are particularly attractive for capturing multi-mode subspace structures in high-dimensional data. Existing recovery methods either operate on the full tensor variable with expensive tensor projections, or adopt factorized formulations that still rely on full-gradient computations, while most stochastic factorized approaches are restricted to tensor decomposition settings. In this work, we propose a stochastic alternating minimization algorithm that operates directly on the core tensor and factor matrices under a Tucker factorization. The proposed method avoids repeated tensor projections and enables efficient mini-batch updates on low-dimensional tensor factors. Numerical experiments on synthetic tensor sensing demonstrate that the proposed algorithm exhibits favorable convergence behavior in wall-clock time compared with representative stochastic tensor recovery baselines.
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