Results 21 to 30 of about 1,788,984 (247)
On Dropout and Nuclear Norm Regularization
CoRR, 2019 We give a formal and complete characterization of the explicit regularizer induced by dropout in deep linear networks with squared loss. We show that (a) the explicit regularizer is composed of an $\ell_2$-path regularizer and other terms that are also re-scaling invariant, (b) the convex envelope of the induced regularizer is the squared nuclear norm ...
Poorya Mianjy, Raman Arora
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Numerical stability and tensor nuclear norm
Numerische Mathematik, 2023 25 pages, 7 ...
Zhen Dai, Lek-Heng Lim
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Nuclear norm of higher-order tensors [PDF]
, 2016 We establish several mathematical and computational properties of the nuclear norm for higher-order tensors. We show that like tensor rank, tensor nuclear norm is dependent on the choice of base field --- the value of the nuclear norm of a real 3-tensor ...
Shmuel Friedland (7936745) +1 more
core +2 more sources
Low-Rank Tensor Completion by Sum of Tensor Nuclear Norm Minimization
IEEE Access, 2019 In this paper, we study the problem of low-rank tensor completion with the purpose of recovering a low-rank tensor from a tensor with partial observed items. To date, there are several different definitions of tensor ranks.
Yaru Su, Xiaohui Wu, Wenxi Liu
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NON-LINEAR MULTI-FRAME IMAGE DENOISING USING WEIGHTED NUCLEAR NORM MINIMIZATION [PDF]
The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, 2021 We address the problem of constructing single low noise image from a sequence of multiple noisy images. We use the approach based on finding and averaging similar blocks in the image and extend it to multiple images.
A. V. Nasonov +2 more
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Spectral Norm and Nuclear Norm of a Third Order Tensor
CoRR, 2019 The spectral norm and the nuclear norm of a third order tensor play an important role in the tensor completion and recovery problem. We show that the spectral norm of a third order tensor is equal to the square root of the spectral norm of three positive semi-definite biquadratic tensors, and the square roots of the nuclear norms of those three ...
Liqun Qi 0001, Shenglong Hu
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Geometry of factored nuclear norm regularization
CoRR, 2017 This work investigates the geometry of a nonconvex reformulation of minimizing a general convex loss function $f(X)$ regularized by the matrix nuclear norm $\|X\|_*$. Nuclear-norm regularized matrix inverse problems are at the heart of many applications in machine learning, signal processing, and control.
Li, Qiuwei, Zhu, Zhihui, Tang, Gongguo
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Dynamic Cardiac MRI Reconstruction Using Combined Tensor Nuclear Norm and Casorati Matrix Nuclear Norm Regularizations [PDF]
, 2022 Low-rank tensor models have been applied in accelerating dynamic magnetic resonance imaging (dMRI). Recently, a new tensor nuclear norm based on t-SVD has been proposed and applied to tensor completion.
Hu, Yue, Zhang, Yinghao
core +1 more source
IEEE Access, 2018 Magnetic resonance spectroscopy (MRS) has many important applications in medical imaging, biology, and chemistry. The 1-D MRS is too crowded for complex samples to retrieve chemical or biological information.
Di Guo, Xiaobo Qu
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Nuclear norm of higher-order tensors
Mathematics of Computation, 2017 23 ...
Shmuel Friedland, Lek-Heng Lim
openaire +4 more sources