基于Householder反射的快速结构化正交字典学习
Fast Structured Orthogonal Dictionary Learning using Householder Reflections
AI总结：
针对结构化正交字典学习问题，提出基于Householder矩阵及少量Householder矩阵乘积的算法，理论上保证l∞范数近似恢复且计算复杂度最优，样本受限场景下性能优于现有方法且计算效率更高。
摘要：
本文提出并研究了结构化正交字典学习问题的算法。首先，我们研究了字典为Householder矩阵的情形，给出了样本复杂度结果，并证明了在l∞范数意义下具有理论保证的近似恢复，且计算复杂度达到最优。随后，我们尝试将这些技术推广到字典为少量Householder矩阵乘积的情况。我们在样本受限场景下对这些技术进行了数值验证，结果表明其性能与现有技术相当甚至更优，同时计算复杂度大幅提升。
英文摘要：
In this paper, we propose and investigate algorithms for the structured orthogonal dictionary learning problem. First, we investigate the case when the dictionary is a Householder matrix. We give sample complexity results and show theoretically guaranteed approximate recovery (in the $l_{\infty}$ sense) with optimal computational complexity. We then attempt to generalize these techniques when the dictionary is a product of a few Householder matrices. We numerically validate these techniques in the sample-limited setting to show performance similar to or better than existing techniques while having much improved computational complexity.
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