连续字典满足低秩张量近似
Continuous dictionaries meet low-rank tensor approximations
摘要：
在这篇简短的论文中，我们桥接了两个看似无关的稀疏近似主题：连续稀疏编码和低秩近似。我们表明，对于一个特定的连续字典的选择，线性系统与核范数正则化有相同的解决方案作为一个BLASSO问题。虽然这一事实已经部分理解的矩阵的情况下，我们进一步表明，张量数据，使用BLASSO求解器的低秩近似问题导致一个新的分支的优化方法，但大大未开发。特别是，建议弗兰克-沃尔夫算法展示了一个自动张量秩选择问题。
英文摘要：
In this short paper we bridge two seemingly unrelated sparse approximation topics: continuous sparse coding and low-rank approximations. We show that for a specific choice of continuous dictionary, linear systems with nuclear-norm regularization have the same solutions as a BLasso problem. Although this fact was already partially understood in the matrix case, we further show that for tensor data, using BLasso solvers for the low-rank approximation problem leads to a new branch of optimization methods yet vastly unexplored. In particular, the proposed Frank-Wolfe algorithm is showcased on an automatic tensor rank selection problem.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
