scholarly journals Random Perturbations of Matrix Polynomials

2020 ◽  
Author(s):  
Patryk Pagacz ◽  
Michał Wojtylak
Keyword(s):  
Matrix Polynomial ◽  
Low Rank ◽  
Random Perturbations ◽  
Random Polynomial ◽  
Wigner Matrix ◽  
Matrix Polynomials ◽  
Rank Matrix ◽  
Special Matrix ◽  
Low Rank Matrix ◽  
Deterministic Limit

Abstract A sum of a large-dimensional random matrix polynomial and a fixed low-rank matrix polynomial is considered. The main assumption is that the resolvent of the random polynomial converges to some deterministic limit. A formula for the limit of the resolvent of the sum is derived, and the eigenvalues are localised. Four instances are considered: a low-rank matrix perturbed by the Wigner matrix, a product HX of a fixed diagonal matrix H and the Wigner matrix X and two special matrix polynomials of higher degree. The results are illustrated with various examples and numerical simulations.

Semi-Orthogonal Low-Rank Matrix Factorization for Deep Neural Networks

2018 ◽  
Author(s):  
Daniel Povey ◽  
Gaofeng Cheng ◽  
Yiming Wang ◽  
Ke Li ◽  
Hainan Xu ◽  
...  
Keyword(s):  
Neural Networks ◽  
Matrix Factorization ◽  
Deep Neural Networks ◽  
Low Rank ◽  
Rank Matrix ◽  
Low Rank Matrix

Adaptive Local Low-rank Matrix Approximation for Recommendation

2019 ◽  
Vol 37 (4) ◽  
pp. 1-34 ◽  
Author(s):  
Huafeng Liu ◽  
Liping Jing ◽  
Yuhua Qian ◽  
Jian Yu
Keyword(s):  
Low Rank ◽  
Matrix Approximation ◽  
Rank Matrix ◽  
Low Rank Matrix ◽  
Low Rank Matrix Approximation

scholarly journals Single-cell data clustering based on sparse optimization and low-rank matrix factorization

2021 ◽  
Author(s):  
Yinlei Hu ◽  
Bin Li ◽  
Falai Chen ◽  
Kun Qu
Keyword(s):  
Single Cell ◽  
Rna Sequencing ◽  
Matrix Factorization ◽  
Data Clustering ◽  
Cell Types ◽  
Low Rank ◽  
Sequencing Data ◽  
Rank Matrix ◽  
Single Cell Rna Sequencing ◽  
Low Rank Matrix

Abstract Unsupervised clustering is a fundamental step of single-cell RNA sequencing data analysis. This issue has inspired several clustering methods to classify cells in single-cell RNA sequencing data. However, accurate prediction of the cell clusters remains a substantial challenge. In this study, we propose a new algorithm for single-cell RNA sequencing data clustering based on Sparse Optimization and low-rank matrix factorization (scSO). We applied our scSO algorithm to analyze multiple benchmark datasets and showed that the cluster number predicted by scSO was close to the number of reference cell types and that most cells were correctly classified. Our scSO algorithm is available at https://github.com/QuKunLab/scSO. Overall, this study demonstrates a potent cell clustering approach that can help researchers distinguish cell types in single-cell RNA sequencing data.

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