A super-resolution framework for tensor decomposition
A super-resolution framework for tensor decomposition
复制标题
张量分解的超分辨率框架
DOI：
10.1093/imaiai/iaac002
复制
发表时间：
2022
期刊：
影响因子：
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通讯作者：
Tang, Gongguo
中科院分区：
文献类型：
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作者：
Li, Qiuwei;Ashley, Ashley;Shen, Lixin;Tang, Gongguo
本文考虑了超完备张量分解的超分辨框架。具体地说，我们将张量分解看作恢复球面上狄拉克测度之和的超分辨问题，并通过最小化测度空间上狄拉克测度的连续模拟来解决这一问题。此优化的最佳值定义了张量核范数。类似于超分辨问题中的分离条件，通过显式构造对偶证书，我们发展了张量因子的非相干条件，使它们形成范数极小化连续模拟的唯一最优解。值得注意的是，球上均匀分布的随机张量因子高概率地满足了导出的非相干条件，这意味着随机张量因子的全局可辨识性。
This work considers a super-resolution framework forovercomplete tensor decomposition. Specifically, we view tensor decomposition as a super-resolution problem of recovering a sum of Dirac measures on the sphere and solve it by minimizing a continuous analog of thenorm on the space of measures. The optimal value of this optimization defines the tensor nuclear norm. Similar to the separation condition in the super-resolution problem, by explicitly constructing a dual certificate, we develop incoherence conditions of the tensor factors so that they form the unique optimal solution of the continuous analog ofnorm minimization. Remarkably, the derived incoherence conditions are satisfied with high probability by random tensor factors uniformly distributed on the sphere, implying global identifiability of random tensor factors.