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Questions tagged [tensor-decomposition]

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3 votes
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Apply 3D Operator to Matrix and get new Matrix

Hopefully this question makes sense. 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 ...
Nukesub's user avatar
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0 answers
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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 ...
user1411900's user avatar
2 votes
0 answers
37 views

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 ...
Jules's user avatar
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1 vote
0 answers
162 views

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)} \...
vaspurakan's user avatar
4 votes
0 answers
89 views

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} ...
Geoffrey Irving's user avatar
8 votes
0 answers
176 views

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 $...
drw's user avatar
  • 203
3 votes
1 answer
483 views

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 ...
KF Gauss's user avatar
  • 171
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2 answers
108 views

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 ...
Jimmy's user avatar
  • 11
1 vote
0 answers
214 views

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 ...
CyberPlayerOne's user avatar
1 vote
1 answer
53 views

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 ...
Thangam's user avatar
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1 answer
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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 ...
CyberPlayerOne's user avatar
3 votes
1 answer
277 views

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 ...
CyberPlayerOne's user avatar