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Introduction

Summary of HDR contents
Acknowledgements

About the manuscript

How to read this manuscript
Terminology and Acronyms Reference
Notations
Bibliography

Introduction to rLRA

Low-rank models: survival kit
Nonnegative Regressions: NNLS and NNKL
Alternating Optimization

Theory of rLRA

Summary
Implicit regularization in regularized low-rank approximations
- Balanced and non-Euclidean algorithms for regularized LRA
Identifiability of complete Dictionary Learning
Dictionary-based Low-Rank Approximations

Fast algorithms for rLRA

Summary
Proco-ALS for fast NCPD
Exact Sparse \(\ell_0\) Nonnegative Least Squares
Median Second-Order-Majorant for faster NNLS
Extrapolated BCD algorithms for unconstrained matrix and tensor decompositions
Constrained Coupled Matrix and Tensor Factorization
- Nonnegative Parafac 2
Unrolled MU for data-driven NMF

Applications of rLRA

Summary
Automatic Music Transcription
Single pixel hyperspectral image reconstruction and unmixing

Perspectives and open problems

Numerical Optimization for KL-based Regularized Inverse Problems
Other topics

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By Jeremy E. Cohen

© Copyright 2023.