Questions tagged [tensor-decomposition]
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12 questions
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Apply 3D Operator to Matrix and get new Matrix
I know I can formulate an operator for a vector as a matrix, then apply that matrix to my vector to get a new vector. For example, if I define a left shift operator which shifts all elements left I ...
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Finding block structure of a tensor
Are there any well-known algorithms for partitioning a dense tensor into block-sparse form?
In other words, I need to find a set of non-overlapping blocks that contain all non-zero entries of the ...
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2
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Scaling tensor approximation by symmetric tensor decomposition with SciPy's L-BFGS-B
I am trying to approximate a symmetric tensor of which the values are in the range of [1e-7,1e-4], by a symmetric tensor decomposition of lower rank. For this I am using the L-BFGS-B method in SciPy's ...
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Anisotropic invariant expansion
I am trying to calculate the second and third invariants for a turbulent flow. I have the second order statistics (both transient and averaged). i.e $uu$, $vv$, $ww$, $uv$, $vw$ and $uw$. These are ...
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Tucker factorisation to compare multiple PCA decompositions?
This is an entry-level question for multiway matrix decompositions. I have a set/population $k$ of entities (here biological cells) for each of which I also have a number ($l$) of flavours of length $...
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2
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computing dual matrix trace norm and tensor gradient in python
I'm trying to write the following function in python:
$$
f_\mu(\mathcal X) = f_0(\mathcal X) + \sum_{i = 1}^n \max_{||\mathcal Y_{i(i)}|| \leq1} \alpha_i\langle \mathcal X_{(i)},\mathcal Y_{i(i)} \...
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3
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Is there a reference/source paper for the TUCKER_ALS() in Tensor Toolbox for MATLAB?
TUCKER_ALS computes the best rank-(R1,R2,..,Rn) approximation of tensor X, according to the specified dimensions. I am using MATLAB Tensor Toolbox Version 2.5. I am wondering if I write a paper, how ...
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4
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Optimally conditioned 3-tensor factorization
I have a 3-tensor $A = A_{ijk}$ with each dimension between 9 and 25 (roughly), and an integer $n > 0$. I would like the factor this tensor as
$$A_{ijk} = \sum_{0 \le \alpha \lt n} B_{\alpha i} ...
- 3,969
3
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1
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Algorithm to decompose a sparse unitary matrix into a Kronecker product of smaller unitary matricies
Given some sparse unitary square matrix $A$ ($dim=2^n$ if it matters), is there an algorithm to decompose $A$ into a Kronecker/tensor product of smaller unitary matrices? In other words: decompose ...
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2
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Explain this multivariate differential identity
$$ \frac{\partial|\nabla\phi|^2}{\partial\phi}=-2\nabla\cdot\nabla\phi$$
I would very appreciate that you help me . Please do it in detail, I am quite not good at such problems.
There is something ...
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Any relation between the singular values of each flattening matrices and the core tensor out of Tucker decomposition?
Before I know how to do tucker decomposition, I mistakenly thought the core tensor is only from combining the singular value matrices of the flattening matrices. Yes I know it is not now.
For the ...
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What is the relation between Kruskal tensor and CP decomposition?
In Matlab Tensor Toolbox there is a tensor type called "Kruskal tensors", I found its form is similar to the CP decomposition.
Wikipedia mentioned:
"As such, many of the methods have been ...
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