Fundamental sampling patterns for low-rank multi-view data completion
Fundamental sampling patterns for low-rank multi-view data completion
复制标题
低秩多视图数据完成的基本采样模式
DOI：
10.1016/j.patcog.2020.107307
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发表时间：
2020
影响因子：
8
通讯作者：
Aggarwal, Vaneet
中科院分区：
文献类型：
--
作者：
Ashraphijuo, Morteza;Wang, Xiaodong;Aggarwal, Vaneet
我们考虑多视图数据补全问题，即补全一个矩阵U=[U1| [2]其中给出了U，U 1和U 2的秩。特别是，我们调查的基本条件的采样模式，即，位置的采样条目有限的完整性，这样一个多视图数据给出相应的秩约束。我们提供了一个几何分析的多视图数据的流形结构，将一个以上的秩约束。我们推导出一个概率条件，保证有限的可完成性与高概率的每列的样本数。最后，我们得到了唯一完备性的保证。数值结果表明，降低采样的复杂性时，考虑到多视图结构相比，只有低秩结构的个人意见被考虑在内。然后，我们提出了一个approach使用牛顿的方法，几乎实现这些信息理论界的多视图数据检索利用秩分解和分析在这项工作中。
We consider the multi-view data completion problem, ie, to complete a matrix U=[U 1| U 2] where the ranks of U, U 1, and U 2 are given. In particular, we investigate the fundamental conditions on the sampling pattern, ie, locations of the sampled entries for finite completability of such a multi-view data given the corresponding rank constraints. We provide a geometric analysis on the manifold structure for multi-view data to incorporate more than one rank constraint. We derive a probabilistic condition in terms of the number of samples per column that guarantees finite completability with high probability. Finally, we derive the guarantees for unique completability. Numerical results demonstrate reduced sampling complexity when the multi-view structure is taken into account as compared to when only low-rank structure of individual views is taken into account. Then, we propose an apporach using Newton’s method to almost achieve these information-theoretic bounds for mulit-view data retrieval by taking advantage of the rank decomposition and the analysis in this work.