张量这一概念的核心在于,它是一个数据容器。 张量的维度(秩):Rank/Order: Rank为0、1、2时分别称为标量、向量和矩阵,Rank为3时是3阶张量,Rank大于3时是N阶张量。这些标量、向量、矩阵和张量里每一个元素被称为tensor element(张量的元素),且同一个张量里元素的类型是保持一样的。 0. scalar 标量 0D张量...
将一系列rank-R的tensor打包为一个rank-(R+1)的tensor (整体维度加一) #‘x’ is [1, 4], ‘y’ is [2, 5], ‘z’ is [3, 6] pack([x, y, z]) => [[1, 4], [2, 5], [3, 6]] # 沿着第一维pack pack([x, y, z], axis=1) => [[1, 2, 3], [4, 5, 6]] 等价...
There are two proper tensor rank functions, the max-Tucker rank and the submax-Tucker rank, which are associated with the Tucker decomposition. We define a partial order among tensor rank functions and show that there exists a unique smallest tensor rank function. We introduce the full rank ...
For an Nth-order tensor X, the Tucker rank is defined as rank(X):=[rank(X(1)),rank(X(2)),…,rank(X(N))], where X(i) is the mode-i unfolding of X [20]. Motivated by the practical applications that the nuclear norm is the convex envelope of the matrix rank within the unit...
The rank of matrix which two matrices act right semi -tensorproduct is given. 给出了两个矩阵做右半张量积后矩阵的秩,并且讨论了相关的秩的不等式. 期刊摘选 Tensoralgebra is tied to coordinates. 张量代数则离不开坐标系. 辞典例句 We derive the relations between physical andtensorcomponents. ...
On the best rank-1 and rank-$(Rsb 1,Rsb 2,cdots,Rsb N)$ approximation of higher-order tensors. Lieven De Lathauwer , Bart De Moor , Joos Vandewalle, On the Best Rank-1 and Rank-(R1,R2,. . .,RN) Approximation of Higher-Order Tensors, SIAM... L De Lathauwer,B De Moor,J ...
On the Best Rank-1 Approximation of Higher-Order Supersymmetric Tensors Recently the problem of determining the best, in the least-squares sense, rank-1 approximation to a higher-order tensor was studied and an iterative method... E Kofidis†,PA Regalia‡ - 《Siam Journal on Matrix ...
fromtensorly.decompositionimporttucker# Apply Tucker decompositiontucker_tensor=tucker(tensor,rank=[2,2,2])# Reconstruct the full tensor from the decomposed formtl.tucker_to_tensor(tucker_tensor) We havemany more decompositionsavailable, be sure to check them out!
We review two similar concepts of hierarchical rank of tensors (which extend the matrix rank to higher order tensors): the TT-rank and the H-rank (hierarchical or H-Tucker rank). Based on this notion of rank, one can define a data-sparse representation of tensors involving O(dnk + dk...
from ( select salesMan, product ,amount, rank() over (partition by product order by amount desc ) ranking from sales) where ranking <=10 序表: = sales.group(product).(~.top(-amount;10)) 比较:实现本例最直观的思路是将数据按产品分组,然后再进行分组内的序运算,简单的方法是直接取组内amount...