用张量t-积在线学习字典，提升多维数据重建效果
Online multidimensional dictionary learning
- 基于t-积框架的在线字典学习，适配张量结构
- 引入安德森加速ISTA，显著提升稀疏性处理效率
- 在数据补全等任务中优于现有方法，适合大规模张量分析
字典学习是信号处理和机器学习中广泛使用的技术，旨在将数据表示为过完备字典中少数元素的线性组合。本文提出一种基于t-积框架的字典学习方法，可高效处理多维张量数据。通过适用于张量结构的在线算法解决字典学习问题，并利用改进的加速迭代收缩阈值算法（ISTA）结合安德森加速技术有效应对稀疏性挑战。实验表明，该方法在数据补全等应用中显著优于现有加速技术，尤其在大规模张量数据分析中表现优异，具有广泛应用潜力。
原文摘要 · Abstract (English)
Dictionary learning is a widely used technique in signal processing and machine learning that aims to represent data as a linear combination of a few elements from an overcomplete dictionary. In this work, we propose a generalization of the dictionary learning technique using the t-product framework, enabling efficient handling of multidimensional tensor data. We address the dictionary learning problem through online methods suitable for tensor structures. To effectively address the sparsity problem, we utilize an accelerated Iterative Shrinkage-Thresholding Algorithm (ISTA) enhanced with an extrapolation technique known as Anderson acceleration. This approach significantly improves signal reconstruction results. Extensive experiments prove that our proposed method outperforms existing acceleration techniques, particularly in applications such as data completion. These results suggest that our approach can be highly beneficial for large-scale tensor data analysis in various domains.
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