论文标题
使用低级张量近似的较大和稀疏张量的光谱分区
Spectral Partitioning of Large and Sparse Tensors using Low-Rank Tensor Approximation
论文作者
论文摘要
考虑了张量的大且稀疏的张量的问题，其中张量由一系列邻接矩阵组成。理论是开发的，是光谱图分配的概括。最佳排名-A $（2,2，λ）$近似值是以$λ= 1,2,3 $计算的，分区是从正交矩阵和近似值的核心张量计算得出的。结果表明，如果张量具有一定的降低性结构，那么最佳近似问题的解会显示张量的降低性结构。此外，如果张量接近可还原，则仍然是张量的结构的溶液。合成数据的数值示例证实了理论结果。应用程序张量的实验表明，该方法可用于从大，稀疏和嘈杂的数据中提取相关信息。
The problem of partitioning a large and sparse tensor is considered, where the tensor consists of a sequence of adjacency matrices. Theory is developed that is a generalization of spectral graph partitioning. A best rank-$(2,2,λ)$ approximation is computed for $λ=1,2,3$, and the partitioning is computed from the orthogonal matrices and the core tensor of the approximation. It is shown that if the tensor has a certain reducibility structure, then the solution of the best approximation problem exhibits the reducibility structure of the tensor. Further, if the tensor is close to being reducible, then still the solution of the exhibits the structure of the tensor. Numerical examples with synthetic data corroborate the theoretical results. Experiments with tensors from applications show that the method can be used to extract relevant information from large, sparse, and noisy data.
