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Fast Methods for Denoising Matrix Completion Formulations, with Applications to Robust Seismic Data Interpolation

Aleksandr Aravkin, Rajiv Kumar, Hassan Mansour, Ben Recht, Felix J. Herrmann
2014 SIAM Journal on Scientific Computing  
Recent SVD-free matrix factorization formulations have enabled rank minimization for systems with millions of rows and columns, paving the way for matrix completion in extremely large-scale applications  ...  We show how this weighting can be used in the context of frequency continuation, an essential aspect to seismic data interpolation.  ...  Our method combines the Pareto curve approach for optimizing (BPDN η ) formulations with SVD-free matrix factorization methods.  ... 
doi:10.1137/130919210 fatcat:ru4o62odgffhhkuh5irryoqzxa

Fast methods for denoising matrix completion formulations, with applications to robust seismic data interpolation [article]

Aleksandr Y. Aravkin and Rajiv Kumar and Hassan Mansour and Ben Recht and Felix J. Herrmann
2014 arXiv   pre-print
Recent SVD-free matrix factorization formulations have enabled rank minimization for systems with millions of rows and columns, paving the way for matrix completion in extremely large-scale applications  ...  We show how this weighting can be used in the context of frequency continuation, an essential aspect to seismic data interpolation.  ...  Our method combines the Pareto curve approach for optimizing (BPDN η ) formulations with SVD-free matrix factorization methods.  ... 
arXiv:1302.4886v3 fatcat:topuq2n46jeo3axjrj6wbka73q

A stress-based formulation of the free material design problem with the trace constraint and multiple load conditions

S. Czarnecki, T. Lewiński
2014 Structural And Multidisciplinary Optimization  
This free material design problem is reduced to an equilibrium problem -in two formulations -of an effective body with locking.  ...  The stress-based formulation reduces to minimization of an integral of a certain norm of stress fields over the stress fields which equilibrate the given loads.  ...  The authors express their sincere thanks to Mrs Iwona Malicka for her dedicated work of word-processing and editing the whole manuscript.  ... 
doi:10.1007/s00158-013-1023-5 fatcat:27xx5kbs3zb7rebootsrbohhgu

Robust Decentralized Low-Rank Matrix Decomposition

István Hegedűs, Árpád Berta, Levente Kocsis, András A. Benczúr, Márk Jelasity
2016 ACM Transactions on Intelligent Systems and Technology  
Low-rank matrix approximation is an important tool in data mining with a wide range of applications including recommender systems, clustering, and identifying topics in documents.  ...  To demonstrate the feasibility of our approach, we present trace-based simulations, real smartphone user behavior analysis, and tests over real movie recommender system data.  ...  This is indeed a harder problem: while (X * , Y * ) minimizes (1) , any other pair of matrices (X * R −1 , Y * R T ) will also minimize for any invertible matrix R ∈ R k×k , and Algorithm 2 is free to  ... 
doi:10.1145/2854157 fatcat:wdctwhiuajenlcqyn7v4oedptu

Evolutionary Radial Basis Functions for Credit Assessment

Estefane Lacerda, Andr� C. P. L. F. Carvalho, Ant�nio P�dua Braga, Teresa Bernarda Ludermir
2005 Applied intelligence (Boston)  
It presents an overall view of the problems involved and the different approaches employed to optimize Artificial Neural Networks genetically.  ...  This article discusses a new approach to the design of a particular Artificial Neural Networks model, RBF networks, through Genetic Algorithms.  ...  Alternatively, the shape might be an ellipsoid since it avoids the hypercube corners overlap. For simplicity, the hypercube shape was adopted in this work.  ... 
doi:10.1007/s10791-005-6617-0 fatcat:gfqzhej3pfabjfk625f6dwp66y

Structured low-rank approximation and its applications

Ivan Markovsky
2008 Automatica  
Related problems are rank minimization and structured pseudospectra. ᭧  ...  The data matrix being Hankel structured is equivalent to the existence of a linear time-invariant system that fits the data and the rank constraint is related to a bound on the model complexity.  ...  trade-off curve of Pareto optimal solutions.  ... 
doi:10.1016/j.automatica.2007.09.011 fatcat:tykwfu35lrhcnhsfuevzsmelqm

Optimal Regularization Parameters for General-Form Tikhonov Regularization [article]

Julianne Chung, Malena I. Español, Tuan Nguyen
2014 arXiv   pre-print
For problems where this is not the case, we describe an approach to compute optimal or near-optimal regularization parameters by using operator approximations for the original problem.  ...  We extend the approach to the multi-parameter Tikhonov problem for the case where all the matrices involved are simultaneously diagonalizable.  ...  We compare opt-Tik-SVD, opt-error-SVD, and opt-Tik-GSVD, and provide average reconstruction errors for the validation set in Figure 4 .5. These plots are often referred to as Pareto curves.  ... 
arXiv:1407.1911v1 fatcat:qelqdtvh6baxhlqcblf7iivd7a

A comprehensive survey: Applications of multi-objective particle swarm optimization (MOPSO) algorithm

Soniya Lalwani, Sorabh Singhal, Rajesh Kumar, Nilama Gupta
2013 Transactions on Combinatorics  
An introduction to the key concepts in MOO is followed by the main body of review containing survey of existing work, organized by application area along with their multiple objectives, variants and further  ...  Due to the complexities in such type of problems powerful heuristic techniques were needed, which has been strongly satisfied by Swarm Intelligence (SI) techniques.  ...  Acknowledgments The authors wish to thank the Executive Director, Birla Institute of Scientific Research for the support given during this work. We are thankful to Dr.  ... 
doaj:d067a695f2874248a87829b843ff1df7 fatcat:l2vav6okc5bcdaci3h2hwoktyy

Decomposition into low-rank plus additive matrices for background/foreground separation: A review for a comparative evaluation with a large-scale dataset

Thierry Bouwmans, Andrews Sobral, Sajid Javed, Soon Ki Jung, El-Hadi Zahzah
2017 Computer Science Review  
Minimization (RLRM).  ...  The main goal of these similar problem formulations is to obtain explicitly or implicitly a decomposition into low-rank matrix plus additive matrices.  ...  Acknowledgment The authors would like to thank the following researchers: Zhouchen Lin (Visual Computing Group, Microsoft Research Asia) who has kindly provided the solver LADMAP [192] and the l 1 -filtering  ... 
doi:10.1016/j.cosrev.2016.11.001 fatcat:vdh7ic4n6zfkjlccnyiq74z5wu

Diversity Enhancement via Magnitude [article]

Steve Huntsman
2022 arXiv   pre-print
In this paper, we use the recently developed theory of magnitude to construct a gradient flow and similar notions that systematically manipulate finite subsets of Euclidean space to enhance their diversity  ...  ACKNOWLEDGMENT Thanks to Andy Copeland, Megan Fuller, Zac Hoffman, Rachelle Horwitz-Martin, and Daryl St.  ...  A rough sketch of this approach is to compute a SVD of the IJE, then use this in turn to estimate the rank. If the rank is not full, then revise the IJE as follows.  ... 
arXiv:2201.10037v1 fatcat:gtu66dbvszegnbpdgjx4ohmcwe

Pareto Optimality in Organelle Energy Metabolism Analysis

Claudio Angione, Giovanni Carapezza, Jole Costanza, Pietro Lio, Giuseppe Nicosia
2013 IEEE/ACM Transactions on Computational Biology & Bioinformatics  
We report that Pareto fronts represent an asymptotic analysis useful to describe the metabolism of an organism aimed at maximizing concurrently two or more metabolite concentrations.  ...  In this paper, we make use of the Pareto-front analysis to investigate the optimization of energy metabolism in mitochondria and chloroplasts.  ...  The Pareto curve can be useful to analyze the trend of the mitochondrial processes that have to satisfy specific constraints.  ... 
doi:10.1109/tcbb.2013.95 pmid:24334395 fatcat:tlf3ygiohzhmrm6vcnmv4bwd74

A hybrid approach for litho-facies characterization in the framework of sequence stratigraphy: A case study from the South Pars gas field, the Persian Gulf basin

Ebrahim Sfidari, Ali Kadkhodaie-Ilkhchi, Hossain Rahimpour-Bbonab, Behzad Soltani
2014 Journal of Petroleum Science and Engineering  
The current study proposes a two-step approach for pore facies characterization in the carbonate reservoirs with an example from the Kangan and Dalan formations in the South Pars gas field.  ...  Moreover, multi-objective genetic algorithms (GAs) are used to evolutionary design of GMDH-type neural networks.  ...  Smaller pore throats result in an increase in the slope of the MICP curves.  ... 
doi:10.1016/j.petrol.2014.06.013 fatcat:tijcfpd4bfgf7nhw5mg3ocp3ca

Case study on wavelet choice based on statistical image quality measures

Igor VUJOVIC, Ivica KUZMANIC
2017 Turkish Journal of Electrical Engineering and Computer Sciences  
Different wavelets are found to be an optimal choice for different weights of the objectives.  ...  This paper proposes a multiobjective approach to selection of wavelets based on two main objectives: statistical image quality measures and execution time.  ...  Dual-tree DWT is used in video coding [4] and a multiobjective approach to choose an optimum subband.  ... 
doi:10.3906/elk-1602-218 fatcat:jvlnpyepsjckvijvn4qnbkl6x4

Intelligence, physics and information – the tradeoff between accuracy and simplicity in machine learning [article]

Tailin Wu
2020 arXiv   pre-print
Fourthly, to make models more robust to label noise, we introduce Rank Pruning, a robust algorithm for classification with noisy labels.  ...  We address part of this question by introducing an algorithm that combines prediction and minimizing information from the input, for exploratory causal discovery from observational time series.  ...  We use noisy label to mimic realistic settings where the data may be noisy and also to have controllable difficulty for different classes.  ... 
arXiv:2001.03780v2 fatcat:piduzlhoafcjhhsgthulbbhtke

Bubblewrap: Online tiling and real-time flow prediction on neural manifolds [article]

Anne Draelos, Pranjal Gupta, Na Young Jun, Chaichontat Sriworarat, John Pearson
2021 arXiv   pre-print
Existing approaches, primarily based on dynamical systems, require strong parametric assumptions that are easily violated in the noise-dominated regime and do not scale well to the thousands of data channels  ...  While most classic studies of function in experimental neuroscience have focused on the coding properties of individual neurons, recent developments in recording technologies have resulted in an increasing  ...  reduced-rank SVD (Appendix A).  ... 
arXiv:2108.13941v2 fatcat:7uedsvpaxzb5biz37jkql2qbia
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