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Low Rank Regularization: A review [PDF]
Neural Networks, 2021 Low rank regularization, in essence, involves introducing a low rank or approximately low rank assumption for matrix we aim to learn, which has achieved great success in many fields including machine learning, data mining and computer version. Over the last decade, much progress has been made in theories and practical applications.
Zhanxuan Hu +3 more
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Low-rank Parareal: a low-rank parallel-in-time integrator
BIT Numerical Mathematics, 2023 AbstractIn this work, the Parareal algorithm is applied to evolution problems that admit good low-rank approximations and for which the dynamical low-rank approximation (DLRA) can be used as time stepper. Many discrete integrators for DLRA have recently been proposed, based on splitting the projected vector field or by applying projected Runge–Kutta ...
Carrel, Benjamin +2 more
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CoRR, 2021 We consider the problem of forecasting multiple values of the future of a vector time series, using some past values. This problem, and related ones such as one-step-ahead prediction, have a very long history, and there are a number of well-known methods for it, including vector auto-regressive models, state-space methods, multi-task regression, and ...
Shane T. Barratt +2 more
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Low rank phase retrieval [PDF]
2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2017 To appear in IEEE Trans.
Seyedehsara Nayer +2 more
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IET Signal Processing, 2022 Abstract Isomap is a well‐known nonlinear dimensionality reduction method that highly suffers from computational complexity. Its computational complexity mainly arises from two stages; a) embedding a full graph on the data in the ambient space, and b) a complete eigenvalue decomposition.
Eysan Mehrbani, Mohammad Hossein Kahaei
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Beyond low rank + sparse: Multi-scale low rank matrix decomposition [PDF]
2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2016 We present a natural generalization of the recent low rank + sparse matrix decomposition and consider the decomposition of matrices into components of multiple scales. Such decomposition is well motivated in practice as data matrices often exhibit local correlations in multiple scales.
Frank Ong, Michael Lustig
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Low‐rank magnetic resonance fingerprinting [PDF]
Medical Physics, 2016 PurposeMagnetic resonance fingerprinting (MRF) is a relatively new approach that provides quantitative MRI measures using randomized acquisition. Extraction of physical quantitative tissue parameters is performed offline, without the need of patient presence, based on acquisition with varying parameters and a dictionary generated according to the Bloch
Mazor, Gal +3 more
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Generalized Low Rank Models [PDF]
Foundations and Trends® in Machine Learning, 2016 Principal components analysis (PCA) is a well-known technique for approximating a tabular data set by a low rank matrix. Here, we extend the idea of PCA to handle arbitrary data sets consisting of numerical, Boolean, categorical, ordinal, and other data types.
Madeleine Udell +3 more
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Low-Rank Sinkhorn Factorization
CoRR, 2021 Several recent applications of optimal transport (OT) theory to machine learning have relied on regularization, notably entropy and the Sinkhorn algorithm. Because matrix-vector products are pervasive in the Sinkhorn algorithm, several works have proposed to \textit{approximate} kernel matrices appearing in its iterations using low-rank factors ...
Meyer Scetbon +2 more
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