Neural Networks

Maolin Che and Yimin Wei
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Maolin Che: Southwestern University of Finance and Economics, School of Economics Mathematics
Yimin Wei: Fudan University, School of Mathematical Sciences

Chapter Chapter 6 in Theory and Computation of Complex Tensors and its Applications, 2020, pp 147-186 from Springer

Abstract: Abstract We focus on the rank-one approximation problem of a tensor A ∈ ℝ I 1 × I 2 × ⋯ × I N $$\mathcal {A}\in \mathbb {R}^{I_1\times I_2\times \dots \times I_N}$$ by neural networks: finding a real scalar σ and N unit x n ∈ ℝ I n $${\mathbf {x}}_n\in \mathbb {R}^{I_n}$$ to minimize ∑ i 1 = 1 I 1 ∑ i 2 = 1 I 2 … ∑ i N = 1 I N [ a i 1 i 2 … i N − σ ⋅ ( x 1 , i 1 x 2 , i 2 … x N , i N ) ] 2 , $$\displaystyle \sum _{i_1=1}^{I_1}\sum _{i_2=1}^{I_2}\dots \sum _{i_N=1}^{I_N}[a_{i_1i_2\dots i_N}-\sigma \cdot (x_{1,i_1}x_{2,i_2}\dots x_{N,i_N})]^2, $$ where x n , i n $$x_{n,i_n}$$ is the i nth element of x n ∈ ℝ I n $${\mathbf {x}}_n\in \mathbb {R}^{I_n}$$ for all i n and n, and σ > 0 is a scaling factor.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-15-2059-4_6

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DOI: 10.1007/978-981-15-2059-4_6

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