An algorithm is presented for decomposing a symmetric tensor into a sum of rank-1 symmetric tensors. For a given tensor, by using apolarity, catalecticant matrices and the condition that the mapping matrices are commutative, the rank of the tensor can be obtained by iteration. Then we can ...
The tensor rank decomposition, or canonical polyadic decomposition, is the decomposition of a tensor into a sum of rank-1 tensors. The condition number of the tensor rank decomposition measures the sensitivity of the rank-1 summands with respect to structured perturbations. Those are perturbations ...
We discuss the non-uniqueness of the rank 1 tensor decomposition for rank 4 tensors of format m 1 × ⋯ × m k , k ≥ 3 . We discuss several classes of examples and provide a complete classification if m 1 = m 2 = 4 . Keywords: tensor rank; rank 1 tensor decomposition; Segre...
Although there has been some work on low-rank models for tensorial data, such as [5,6,12,13,18,19], the “rank” of tensors they have used are far from satisfactory. Although CP decomposition [9] based tensor rank is a natural generalization of matrix rank, unfortunately it is not in...
Tensor rank decomposition
Cichocki, "Big data singular value decom- position based on low-rank tensor train decomposition," RIKEN BSI, Tech. Rep., 2014 (submitted).N. Lee and A. Cichocki. Big data matrix singular value decomposition based on low-rank tensor train decomposition. In Advances in Neural Networks, pages ...
张量环式分解 (tensor ring decompsition, TR decomposition) 是一种特殊的张量分解结构,相比于常用的CP分解和Tucker分解,这种分解结构可以挖掘和表达更多的数据模式,但与常用的张量分解低秩结构一样,随着数据张量的阶数增加,找到一个合理低秩结构 (latent TR factors, 简称“隐性TR因子”) 的难度也会相应地增加。
Moreover, the tensor singular value decomposition (SVD) and the tubal rank and multi-rank of a tensor were proposed based on the tensor-tensor product in the Fourier domain [17]. In order to maintain the intrinsic structure of the tensor data, Semerci et al. [38] proposed a tensor ...
En route to our new data structure design, we establish an interesting connection between succinct data structures and approximate nonnegative tensor decomposition. Our connection shows that for specific problems, to construct a space-efficient data structure, it suffices to approximate a particular ...
In addition to the selection of (local) approximation spaces of a certain degree (in the spirit of “p-refinement”), we introduce a spatial decomposition of the density representation into layers (similar to “h-refinement”) around some center of mass of the considered density. This enables...