Quantum machine learning: a classical perspective
Recently, increased computational power and data availability, as well as algorithmic
advances, have led machine learning (ML) techniques to impressive results in regression …
advances, have led machine learning (ML) techniques to impressive results in regression …
Complete dictionary recovery over the sphere I: Overview and the geometric picture
We consider the problem of recovering a complete (ie, square and invertible) matrix A 0,
from Y∈ R n× p with Y= A 0 X 0, provided X 0 is sufficiently sparse. This recovery problem is …
from Y∈ R n× p with Y= A 0 X 0, provided X 0 is sufficiently sparse. This recovery problem is …
Tensor robust principal component analysis with a new tensor nuclear norm
In this paper, we consider the Tensor Robust Principal Component Analysis (TRPCA)
problem, which aims to exactly recover the low-rank and sparse components from their sum …
problem, which aims to exactly recover the low-rank and sparse components from their sum …
Low-rank high-order tensor completion with applications in visual data
Recently, tensor Singular Value Decomposition (t-SVD)-based low-rank tensor completion
(LRTC) has achieved unprecedented success in addressing various pattern analysis issues …
(LRTC) has achieved unprecedented success in addressing various pattern analysis issues …
[图书][B] Tensor analysis: spectral theory and special tensors
L Qi, Z Luo - 2017 - SIAM
Matrix theory is one of the most fundamental tools of mathematics and science, and a
number of classical books on matrix analysis have been written to explore this theory. As a …
number of classical books on matrix analysis have been written to explore this theory. As a …
Tensor robust principal component analysis: Exact recovery of corrupted low-rank tensors via convex optimization
This paper studies the Tensor Robust Principal Component (TRPCA) problem which
extends the known Robust PCA to the tensor case. Our model is based on a new tensor …
extends the known Robust PCA to the tensor case. Our model is based on a new tensor …
A geometric analysis of phase retrieval
Can we recover a complex signal from its Fourier magnitudes? More generally, given a set
of m measurements, y_k=\left| a _k^* x\right| yk= ak∗ x for k= 1, ..., mk= 1,…, m, is it possible …
of m measurements, y_k=\left| a _k^* x\right| yk= ak∗ x for k= 1, ..., mk= 1,…, m, is it possible …
Exact tensor completion using t-SVD
In this paper, we focus on the problem of completion of multidimensional arrays (also
referred to as tensors), in particular three-dimensional (3-D) arrays, from limited sampling …
referred to as tensors), in particular three-dimensional (3-D) arrays, from limited sampling …
Efficient tensor completion for color image and video recovery: Low-rank tensor train
This paper proposes a novel approach to tensor completion, which recovers missing entries
of data represented by tensors. The approach is based on the tensor train (TT) rank, which is …
of data represented by tensors. The approach is based on the tensor train (TT) rank, which is …
Tensor factorization for low-rank tensor completion
Recently, a tensor nuclear norm (TNN) based method was proposed to solve the tensor
completion problem, which has achieved state-of-the-art performance on image and video …
completion problem, which has achieved state-of-the-art performance on image and video …