منابع مشابه
Trees and Tensors on Kähler Manifolds
We present an organized method to convert between partial derivatives of metrics (functions) and covariant derivatives of curvature tensors (functions) on Kähler manifolds. Basically it reduces the highly recursive computation in tensor calculus to the enumeration of certain trees with external legs.
متن کاملGeneralized Multilinear Model for Dimensionality Reduction of Binary Tensors
Generalized multilinear model for dimensionality reduction of binary tensors (GMM-DR-BT) is a technique for computing low-rank approximations of multi-dimensional data objects, tensors. The model exposes a latent structure that represents dominant trends in the binary tensorial data while retaining as much information as possible. Recently, there exist several models for computing the low-rank ...
متن کاملDimensional Reduction of Conformal Tensors and Einstein–Weyl Spaces⋆
Conformal Weyl and Cotton tensors are dimensionally reduced by a Kaluza– Klein procedure. Explicit formulas are given for reducing from four and three dimensions to three and two dimensions, respectively. When the higher dimensional conformal tensor vanishes because the space is conformallly flat, the lower-dimensional Kaluza–Klein functions satisfy equations that coincide with the Einstein–Wey...
متن کاملVectorial Dimension Reduction for Tensors Based on Bayesian Inference
Dimensionality reduction for high-order tensors is a challenging problem. In conventional approaches, higher order tensors are “vectorized” via Tucker decomposition to obtain lower order tensors. This will destroy the inherent high-order structures or resulting in undesired tensors, respectively. This paper introduces a probabilistic vectorial dimensionality reduction model for tensorial data. ...
متن کاملCanonical Polyadic Decomposition of Third-Order Tensors: Reduction to Generalized Eigenvalue Decomposition
Now, the statement (i) follows from (S.1.3) by setting y = x. (ii) Since the vectors ci1 , . . . , ciK−1 are linearly independent in R , it follows that there exists a vector y such that det [ ci1 . . . ciK−1 y ] 6= 0. Hence, by (S.1.3), the (i1, . . . , iK−1)-th column of B(C) is nonzero. (iii) follows from (S.1.3) and the fact that det [ ci1 . . . ciK−1 y ] = 0 if and only if y ∈ span{ci1 , ....
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 2005
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.2049168