论文标题
连续词典符合低级张量近似值
Continuous dictionaries meet low-rank tensor approximations
论文作者
论文摘要
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：连续的稀疏编码和低级近似值。我们表明，对于连续词典的特定选择，具有核电 - 正则化的线性系统具有与Blasso问题相同的解决方案。尽管在矩阵案例中已经部分理解了这一事实，但我们进一步表明，对于张量数据，使用blasso求解器进行低级别近似问题导致了优化方法的新分支，但尚未探索。特别是，在自动张量排名的选择问题上展示了拟议的Frank-Wolfe算法。
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.
