Matrix factorization techniques in machine learning, signal processing, and statistics

KL Du, MNS Swamy, ZQ Wang, WH Mow - Mathematics, 2023 - mdpi.com
Compressed sensing is an alternative to Shannon/Nyquist sampling for acquiring sparse or
compressible signals. Sparse coding represents a signal as a sparse linear combination of …

Cross tensor approximation methods for compression and dimensionality reduction

S Ahmadi-Asl, CF Caiafa, A Cichocki, AH Phan… - IEEE …, 2021 - ieeexplore.ieee.org
Cross Tensor Approximation (CTA) is a generalization of Cross/skeleton matrix and CUR
Matrix Approximation (CMA) and is a suitable tool for fast low-rank tensor approximation. It …

Learned robust PCA: A scalable deep unfolding approach for high-dimensional outlier detection

HQ Cai, J Liu, W Yin - Advances in Neural Information …, 2021 - proceedings.neurips.cc
Robust principal component analysis (RPCA) is a critical tool in modern machine learning,
which detects outliers in the task of low-rank matrix reconstruction. In this paper, we propose …

Robust CUR decomposition: Theory and imaging applications

HQ Cai, K Hamm, L Huang, D Needell - SIAM Journal on Imaging Sciences, 2021 - SIAM
This paper considers the use of robust principal component analysis (RPCA) in a CUR
decomposition framework and applications thereof. Our main algorithms produce a robust …

Tensor CUR decomposition under T-product and its perturbation

J Chen, Y Wei, Y Xu - Numerical Functional Analysis and …, 2022 - Taylor & Francis
In order to process the large-scale data, a useful tool in dimensionality reduction of a matrix,
the CUR decomposition has been developed, which can compress the huge matrix with its …

Matrix completion with cross-concentrated sampling: Bridging uniform sampling and CUR sampling

HQ Cai, L Huang, P Li, D Needell - IEEE Transactions on …, 2023 - ieeexplore.ieee.org
While uniform sampling has been widely studied in the matrix completion literature, CUR
sampling approximates a low-rank matrix via row and column samples. Unfortunately, both …

Kernel matrix approximation on class-imbalanced data with an application to scientific simulation

P Hajibabaee, F Pourkamali-Anaraki… - IEEE …, 2021 - ieeexplore.ieee.org
Generating low-rank approximations of kernel matrices that arise in nonlinear machine
learning techniques holds the potential to significantly alleviate the memory and …

Fast robust tensor principal component analysis via fiber CUR decomposition

HQ Cai, Z Chao, L Huang… - Proceedings of the IEEE …, 2021 - openaccess.thecvf.com
We study the problem of tensor robust principal component analysis (TRPCA), that aims to
separate an underlying low-multilinear-rank tensor and a sparse outlier tensor from their …

Fast cross tensor approximation for image and video completion

S Ahmadi-Asl, MG Asante-Mensah, A Cichocki… - Signal Processing, 2023 - Elsevier
This paper presents a framework that suggests the utilization of cross tensor approximation
or tensor CUR approximation to reconstruct incomplete images and videos. The proposed …

Tensor Robust CUR for Compression and Denoising of Hyperspectral Data

MM Salut, DV Anderson - IEEE Access, 2023 - ieeexplore.ieee.org
Hyperspectral images are often contaminated with noise which degrades the quality of data.
Recently, tensor robust principal component analysis (TRPCA) has been utilized to remove …