Rank-one approximationRank-two tensorsIt is shown that the relative distance in Frobenius norm of a real symmetric order-dtensor of rank-two to its best rank-one approximation is upper bounded by1-(1-1/d)d-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\...
三阶张量,就是order为3的张量。 为了方便自己区分,我将张量的在每个方向上的大小称为维度,例如:3*4*5。2、rankrank称为张量的秩。Rank-one Tensors:如果一个N阶张量可以表示成N个向量的外积,那么这个张量的秩为1。TensorRank:将张量分解成秩1张量,秩1张量的最小数称为张量的秩。
Approximation of High-Dimensional Rank One TensorsQuery algorithmsHigh-dimensional approximationSeparable functionsRate of approximationMany real world problems are high-dimensional in that their solution is a function which depends on many variables or parameters. This presents a computational challenge since...
Based on the above equivalence property, three relaxation approaches for solving the best rank-1 tensor approximation problems are proposed, including two convex relaxations and a nonconvex one. The two convex relaxations utilize the matrix nuclear norm regularization/constraints. They have the advantage...
We need to check that at each step the tensor μ ( q ) in the definition of a linear projection from a point with respect to one of the factors is not only concise, but it also has rank 4 and not lower rank. Concision was proved in Section 2.1. In our case, with n 1 = 3 ,...
From this perspective, a rank-2 tensor (one that requires numbers to describe) is equivalent, mathematically, to an matrix. rank object 0 scalar 1 vector 2 matrix tensor The above table gives the most common nomenclature associated to tensors of various rank. Some care must be exhibited, ...
We show that sums of rank one tensors (or separable functions) representing the so-called Candecomp/Parafac or CP-decomposition is used effectively to solve the chemical master equations as in many cases the effective tensor rank of the probability distribution only grows slowly with time. Both ...
而“site_id”为IdFeature,源数据为string类型,通过hash的方法得到特征的id值,one-hot或dict索引的方式检索embedding特征矩阵,得到相应特征。这里hash_bucket_size为hash bucket的大小,有冲突可能。对于user_id等规模比较大的,hash冲突影响比较小的特征, ℎ ℎ\_ \_ =\frac{ \_ \_ }{ratio},建议ratio\in...
tensor inmachine learning algorithmsis the rank of two, referred to as a matrix; for example, a matrix can be a suitable structure for image representation where each entry presents one pixel. A video can be represented as a three-dimensional tensor where the first two dimensions represent a ...
Face Recognition using Discriminatively Trained Orthogonal Rank One Tensor Projections We propose a method for face recognition based on a discriminative linear projection. In this formulation images are treated as tensors, rather than the mo... H Gang,PA Viola,SM Drucker - IEEE 被引量: 122发表...