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Secrets of Matrix Factorization: Approximations, Numerics, Manifold Optimization and Random Restarts

Je Hyeong Hong, Andrew Fitzgibbon
2015 2015 IEEE International Conference on Computer Vision (ICCV)  
Matrix factorization (or low-rank matrix completion) with missing data is a key computation in many computer vision and machine learning tasks, and is also related to a broader class of nonlinear optimization  ...  This paper provides a unified derivation of a number of recent approaches, so that similarities and differences are easily observed.  ...  Acknowledgements The work was supported by Microsoft and Toshiba Research Europe. We thank Roberto Cipolla, Christopher Zach, Bamdev Mishra and the anonymous reviewers for their invaluable comments.  ... 
doi:10.1109/iccv.2015.470 dblp:conf/iccv/HongF15 fatcat:obhjrzrw6zcvrldiaymlwvzofy

Snail Transcription Factors [chapter]

Amparo Cano, M. Angela Neto
2011 Encyclopedia of Cancer  
SAHA Definition Suberoylanilide hydroxamic acid, an inhibitor of histone deacetylases. ▶ Vorinostat M. Schwab (ed.), Encyclopedia of Cancer,  ...  Structure Determination and Modeling The optimization of the compounds is either at random using the intuition of the medicinal chemist or now increasingly based on the intimate structural knowledge of  ...  , matrix metalloproteinase, cytosolic and mitochondrial ▶ glutathione level, and other cancer-relevant factors.  ... 
doi:10.1007/978-3-642-16483-5_5389 fatcat:gmjzxqp2u5gljew5l3z7auflpq

One Bit is All It Takes: A Devastating Timing Attack on BLISS's Non-Constant Time Sign Flips

Mehdi Tibouchi, Alexandre Wallet
2020 Journal of Mathematical Cryptology  
The bimodal Gaussian distribution that BLISS is named after is achieved using a random sign flip during signature generation, and neither the original implementation of BLISS nor strongSwan ensure that  ...  The recovery is carried out using a maximum likelihood estimation on the space of parameters, which can be seen as a statistical manifold.  ...  for the attack of the previous section to succeed and fully recover the secret key.  ... 
doi:10.1515/jmc-2020-0079 fatcat:midtzpmarfcgllljwp6a5yjgt4

Spectral Regularization Algorithms for Learning Large Incomplete Matrices

Rahul Mazumder, Trevor Hastie, Robert Tibshirani
2010 Journal of machine learning research  
, and can fit a rank 40 approximation to the full Netflix training set in 6.6 hours.  ...  Our semidefinite-programming algorithm is readily scalable to large matrices: for example it can obtain a rank-80 approximation of a 10(6) × 10(6) incomplete matrix with 10(5) observed entries in 2.5 hours  ...  Robert Tibshirani was partially supported from National Science Foundation Grant DMS-9971405 and National Institutes of Health Contract N01-HV-28183.  ... 
pmid:21552465 pmcid:PMC3087301 fatcat:ku2kbqnynzbp7ld5os46u6gsgi

14th International Symposium on Mathematical Programming

1990 Mathematical programming  
Finally I report numerical results of a comparison between the variant and a minimization approach using penalty functions.  ...  It is shown that for the success of the variant dom must ful ll a regularity property and that the choice of the normal vectors must meet some demands.Both requirements are ful lled if dom is polyhedral  ...  LU decompositions of submatrices of the diagonal blocks of the main factor in the basic matrix representation improve the numerical stability o f the processes.  ... 
doi:10.1007/bf01580875 fatcat:3jtclwmntzgjxkqs5uecombdaa

Non-intrusive reduced order modeling of nonlinear problems using neural networks

J.S. Hesthaven, S. Ubbiali
2018 Journal of Computational Physics  
Since the accuracy of the resulting discretization heavily relies on these two factors, a direct numerical approximation of the full-order model implies severe computational costs.  ...  However, since reduced bases generally belong to nonlinear, matrix manifolds, standard interpolation techniques may fail, as they cannot enforce the constraints characterizing those manifolds, unless employing  ...  All test cases considered in our numerical studies involved three parameters, affecting either physical or geometrical factors of the differential problem.  ... 
doi:10.1016/ fatcat:c3eb6i5zpjdhnnawvhr6qh5sse

PageRank Beyond the Web

David F. Gleich
2015 SIAM Review  
The mathematics of PageRank, however, are entirely general and apply to any graph or network in any domain.  ...  It's even used for systems analysis of road networks, as well as biology, chemistry, neuroscience, and physics. We'll see the mathematics and ideas that unite these diverse applications.  ...  for carefully reading several early drafts and Yongyang Yu for assistance with the literature review.  ... 
doi:10.1137/140976649 fatcat:odab3aoaqbfddidyh653kn4oem

Tensor decompositions and algorithms, with applications to tensor learning [article]

Felipe Bottega Diniz
2021 arXiv   pre-print
A new algorithm of the canonical polyadic decomposition (CPD) presented here. It features lower computational complexity and memory usage than the available state of the art implementations.  ...  At the end of this chapter we introduce the Tensor Train decomposition and show how to use it to compute higher order CPDs.  ...  We generate random tensors of shape n × n × . . . × n and rank R = 5, where the entries of each factor matrix are drawn from the normal distribution (mean 0 and variance 1).  ... 
arXiv:2110.05997v1 fatcat:jktyucn73rgurg52kh4itgynmi

Understanding Protein Flexibility through Dimensionality Reduction

Miguel L. Teodoro, George N. Phillips, Lydia E. Kavraki
2003 Journal of Computational Biology  
Induced t occurs during the binding of a protein to other proteins, nucleic acids, or small molecules (ligands) and is a critical part of protein function.  ...  It is now widely accepted that conformational changes of proteins can affect their ability to bind other molecules and that any progress in modeling protein motion and exibility will contribute to the  ...  , and a Predoctoral Fellowship from the Keck Center for Computational Biology.  ... 
doi:10.1089/10665270360688228 pmid:12935348 fatcat:rogmclqjv5du3axs367ahz6wnu

Community sense and response systems

Matthew Faulkner, MingHei Cheng, Andreas Krause, Robert Clayton, Thomas Heaton, K. Mani Chandy, Monica Kohler, Julian Bunn, Richard Guy, Annie Liu, Michael Olson
2014 Communications of the ACM  
fit GMMs using EM with 3 random restarts.  ...  However, since it is applied on a much smaller set, it can be initialized using multiple random restarts.  ...  Let Σ −1 = LL T be the Cholesky decomposition of Σ −1 , L = U DV T denote the SVD of L, and D i,i denote the ith entry of the diagonal of D, . copies of g f , and let S be a random sample of A.3 Complexity  ... 
doi:10.1145/2622633 fatcat:zexy7ku2qrej5b3bhq65vgbvva

Quantum Information with Continuous Variable systems [article]

Carles Rodó
2011 arXiv   pre-print
Secondly, its production, manipulation and detection with current optical technology can be done with a very high degree of accuracy and control.  ...  A special class of CV states, are the so-called Gaussian states.  ...  They work as follows: assume that Alice and Bob possess, in advance, a common secret key. This secret key must be exchanged by hand once, and it has to be random and secure.  ... 
arXiv:1005.4694v2 fatcat:lslgg5erzfgwlkdqrky5pwhome

Secure computations on non-integer values

M. Franz, B. Deiseroth, K. Hamacher, S. Jha, S. Katzenbeisser, H. Schroder
2010 2010 IEEE International Workshop on Information Forensics and Security  
This thesis presents new results in this field of research. Conclusions and Future Work 107 References  ...  Since then, this area of research has witnessed many new theoretical results and technological advances, which made it possible to realize a large scale of applications using techniques from SMC.  ...  Numerical computations for eigenvalue or singular value problems, differential equations or matrix inversion constitute important examples of this class of problems.  ... 
doi:10.1109/wifs.2010.5711458 dblp:conf/wifs/FranzDHJ0S10 fatcat:gy3kosjqxrbcbbbpllcmqcpwtu

Machine Learning [chapter]

2014 Encyclopedia of Social Network Analysis and Mining  
Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use.  ...  The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not  ...  Jacobian matrix and is known as the damping factor.  ... 
doi:10.1007/978-1-4614-6170-8_100067 fatcat:dmen3wa2gzd6jnzlxgudyscbm4

Computer and Information Science, Vol. 2, No. 4, November, 2009, Part A

Editor CIS
2009 Computer and Information Science  
Each link is symmetric and the approximate distance of two nodes can be evaluated according to the received signal intensity.  ...  Each node can compute the approximate distance to BS according to the received signal intensity.  ...  In the data extracting, cleaning and loading process, because of the reasons of the system or some unpredictable factors, these activities will often fail, and if the system is restarted after failing,  ... 
doi:10.5539/cis.v2n4p0a fatcat:tgkgoy4mczfevkd42llwzxubl4

Enhancement of Hierarchy Cluster-Tree Routing for Wireless Sensor Network

Xuxing Ding, Fangfang Xie, Qing Wu
2009 Computer and Information Science  
Each link is symmetric and the approximate distance of two nodes can be evaluated according to the received signal intensity.  ...  Each node can compute the approximate distance to BS according to the received signal intensity.  ...  In the data extracting, cleaning and loading process, because of the reasons of the system or some unpredictable factors, these activities will often fail, and if the system is restarted after failing,  ... 
doi:10.5539/cis.v2n4p89 fatcat:nhc7jiwirrhstorva4xsgky4pa
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