Schatten $P$ Norm

The Schatten p-norm is a matrix norm generalizing the nuclear norm (p=1) and Frobenius norm (p=2), used primarily for low-rank matrix approximation and related problems in various fields. Current research focuses on developing efficient algorithms, such as iteratively reweighted methods and those based on Krylov subspaces, to minimize functions involving the Schatten p-norm, often within the context of tensor factorization or other structured data. These advancements improve the speed and accuracy of low-rank matrix recovery in applications like image restoration, multi-view clustering, and data imputation, leading to more efficient and effective solutions in these domains.

Papers

June 22, 2024

Efficient Low-rank Identification via Accelerated Iteratively Reweighted Nuclear Norm Minimization
Hao Wang, Ye Wang, Xiangyu Yang
Low Rank Low Rate ACCELERATION Local Convergence Nuclear Norm Low Rank Matrix Estimation Schatten $P$ Norm

July 24, 2023

A Theoretically Guaranteed Quaternion Weighted Schatten p-norm Minimization Method for Color Image Restoration
Qing-Hua Zhang, Liang-Tian He, Yi-Lun Wang, Liang-Jian Deng, Jun Liu
Color Image Color Image Denoising Quaternion Domain Minimization Algorithm Tensor Norm Schatten $P$ Norm

April 22, 2023

Hyper-Laplacian Regularized Concept Factorization in Low-rank Tensor Space for Multi-view Clustering
Zixiao Yu, Lele Fu, Zhiling Cai, Zhoumin Lu
Multi View Clustering Tensor Clustering Schatten $P$ Norm Concept FacTorization Tensor Subspace

March 29, 2023

Multi-View Clustering via Semi-non-negative Tensor Factorization
Jing Li, Quanxue Gao, Qianqian Wang, Wei Xia, Xinbo Gao
Multi View Clustering Non Negative Matrix Factorization Schatten $P$ Norm

July 18, 2022

Private Convex Optimization in General Norms
Sivakanth Gopi, Yin Tat Lee, Daogao Liu, Ruoqi Shen, Kevin Tian
Stochastic Convex Optimization Learning Norm Private Optimization Private Convex Optimization Schatten $P$ Norm

June 23, 2022

Quantum Approximation of Normalized Schatten Norms and Applications to Learning
Yiyou Chen, Hideyuki Miyahara, Louis-S. Bouchard, Vwani Roychowdhury
LeArning Abstract Financial Application Similarity Measure Fidelity Metric Schatten $P$ Norm Unitary Operation

May 19, 2022

Truncated tensor Schatten p-norm based approach for spatiotemporal traffic data imputation with complicated missing patterns
Tong Nie, Guoyang Qin, Jian Sun
Constructive Approach Complex Pattern Missing Value Tensor Based Spatiotemporal Traffic Tensor Rank Low Rank Tensor Completion Schatten $P$ Norm Traffic Data Imputation

February 10, 2022

Low-Rank Approximation with $1/\epsilon^{1/3}$ Matrix-Vector Products
Ainesh Bakshi, Kenneth L. Clarkson, David P. Woodruff
Average Approximation Low Rank Approximation Spectral Norm Matrix Vector Product Krylov Subspace Schatten $P$ Norm