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Deep-RLS: A Model-Inspired Deep Learning Approach to Nonlinear PCA [article]

Zahra Esmaeilbeig, Shahin Khobahi, Mojtaba Soltanalian
2020 arXiv   pre-print
In particular, we formulate the nonlinear PCA for the blind source separation (BSS) problem and show through numerical analysis that Deep-RLS results in a significant improvement in the accuracy of recovering  ...  In this work, we consider the application of model-based deep learning in nonlinear principal component analysis (PCA).  ...  to improve the recursive least squares solution for nonlinear PCA.  ... 
arXiv:2011.07458v2 fatcat:xwnxgzu7vvai3i2cgparlqzbq4

A class of neural networks for independent component analysis

J. Karhunen, E. Oja, L. Wang, R. Vigario, J. Joutsensalo
1997 IEEE Transactions on Neural Networks  
We consider learning algorithms for each layer, and modify our previous nonlinear PCA type algorithms so that their separation capabilities are greatly improved.  ...  The basic ICA network consists of whitening, separation, and basis vector estimation layers. It can be used for both blind source separation and estimation of the basis vectors of ICA.  ...  ACKNOWLEDGMENT The authors are grateful to the reviewers for their detailed and useful comments.  ... 
doi:10.1109/72.572090 pmid:18255654 fatcat:7ycqgkg5yvdhflruafe75wfaay

On the Relationships between Blind Equalization and Blind Source Separation – Part II: Foundations

R. Attux, A. Neves, L.T. Duarte, R. Suyama, C. Junqueira, L. Rangel, T.M. Dias, J.M.T. Romano
2007 Journal of Communication and Information Systems  
However, in this second part, equivalences between the Benveniste-Goursat-Ruget theorem and the approach to blind source separation based on maximum-likelihood, between the Shalvi-Weinstein techniques  ...  The objective of this two-part work is to present and discuss the relationships between the problems of blind equalization and blind source separation.  ...  ACKNOWLEDGEMENTS The authors thank FAPESP and CNPq for the financial support. Our warmest thanks go to Dr.  ... 
doi:10.14209/jcis.2007.6 fatcat:nthkl4pexjhbrowrb6whj2ig5a

A Review of Independent Component Analysis Techniques and their Applications

DP Acharya, G Panda
2008 IETE Technical Review  
Independent Component Analysis, a computationally efficient blind statistical signal processing technique, has been an area of interest for researchers for many practical applications in various fields  ...  In this work, we present different ICA algorithms from their basics to their potential applications to serve as a comprehensive single source for an inquisitive researcher to carry out his work in this  ...  GA has been used for nonlinear blind source separation in [29, 30] and for noise separation from electrocardiogram signals in [31] .  ... 
doi:10.4103/0256-4602.45424 fatcat:dq3m4vngxvehhgjojpi52or6ly

New blind estimation method of evoked potentials based on minimum dispersion criterion and fractional lower order statistics

Daifeng Zha
2008 Journal of Biomedical Science and Engineering  
Conventional blind separation and estimation method of evoked potentials is based on second order statistics (SOS).  ...  Conventional blind separation and estimation method of evoked potentials is based on second order statistics or high order Statistics.  ...  Conventional blind separation and estimation method of evoked potentials is based on second order statistics.  ... 
doi:10.4236/jbise.2008.12015 fatcat:h7zcjpnsszcr7d6brlgnrfwrzy

Second Order Hebbian Neural Networks And Blind Source Separation

Konstantinos I. Diamantaras
1998 Zenodo  
In particular, Section 2 reviews the use of second order statistics for the blind separation of uncorrelated sources based on similar work proposed for digital communications problems.  ...  If one uses methods based on higher-order statistics (HOS) one assumes that the source samples are independent random variables and that their pdf's are not Gaussian except for perhaps only one source  ... 
doi:10.5281/zenodo.36539 fatcat:jjtv3oy3n5fuzirveaqbruox7a

Harmonic Elimination of Inverters using Blind Signal Separation

B. Justus Rabi, R. Arumugam
2005 American Journal of Applied Sciences  
The harmonic separation process is implemented with a processor achieves low THD using Blind Signal separation. It is mostly used in medical instrumentation and medical applications like ECG, EEG.  ...  With the rapid growth in the utilization of the rectifier for critical loads, e.g. In computer or medical equipment the need for high quality uninterruptible power is increasing.  ...  Linear models of the form (1) are used in several known techniques, but the assumptions are different .In the standard least square method, that the matrix A is completely known.  ... 
doi:10.3844/ajassp.2005.1434.1437 fatcat:wocuz6r6efczfo67rla4vdpsca

A Novel Blind Source Separation Algorithm using Bussgang Criterion and Natural Gradient

Govind Murmu, S. Bhattacharya
2016 Indian Journal of Science and Technology  
Objectives: In this paper, a novel algorithm based on Transform Domain Least Mean Square (TDLMS) is proposed for Blind Source Separation (BSS).  ...  The natural gradient is computed from a cost function based on Bussgang criterion.  ...  Vishnu Priye, Dean, R&D, ISM Dhanbad, for the fruitful discussions and help in writing this paper. References  ... 
doi:10.17485/ijst/2016/v9i39/100365 fatcat:lazrfnfpyvgllophdfoayd2tk4

Neural Network Implementations for PCA and Its Extensions

Jialin Qiu, Hui Wang, Jiabin Lu, Biaobiao Zhang, K.-L. Du
2012 ISRN Artificial Intelligence  
PCA is a statistical method that is directly related to EVD and SVD. Minor component analysis (MCA) is a variant of PCA, which is useful for solving total least squares (TLSs) problems.  ...  These methods are useful in adaptive signal processing, blind signal separation (BSS), pattern recognition, and information compression.  ...  In Section 5, least means squared error-based PCA methods are dealt with. Other optimization-based PCA methods are described in Section 6. PCA based on the anti-Hebbian rule is treated in Section 7.  ... 
doi:10.5402/2012/847305 fatcat:5v5l5v56ozg7lkxfktm5t7cgle

Page 23 of The Journal of Neuroscience Vol. 19, Issue 7 [page]

1999 The Journal of Neuroscience  
PCA-based decomposition methods A second class of proposed LPC decompositions have involved PCA (Donchin, 1966; Glaser and Ruchkin, 1976; Friedman, 1984; Dien et al., 1997).  ...  The current implementation limits the number of data channels (and separated sources) that can be practically separated to ~50 on current computers.  ... 

Independent Component Analysis and Blind Signal Separation: Theory, Algorithms and Applications

Eduardo F. Simas Filho, José M. de Seixas, Natanael N. Moura, Diego B. Haddad, José M. Faier, Maria C. S. Albuquerque
2012 Learning and Nonlinear Models  
An overview on the main statistical principles that guide the search for the independent components is formulated, methods for blind signal separation that require both high-order and second-order statistics  ...  This paper reviews Independent Components Analysis (ICA) and Blind Signal Separation (BSS) problems.  ...  Acknowledgements The authors are thankful for the support provided by CNPq and FAPERJ (Brazil), and for the Brazilian Navy Research Institute (IPqM) for providing the data set used in this work.  ... 
doi:10.21528/lnlm-vol10-no1-art4 fatcat:fewa5i5dozbilbr3euyntf4kvu

A High Order Cumulants Based Multivariate Nonlinear Blind Source Separation Method

Feng Zhang
2005 Machine Learning  
Following the proposed nonlinear model, the blind source separation (BSS) criterion, as a function of high-order cumulants, is shown to produce a block-structured joint cumulant matrix by an orthogonal  ...  The nonlinear patterns are identified by extracting their lower-dimensional manifolds via the principal curves method and then transforming back to the original data space.  ...  Nonlinear blind source separation algorithm Review on linear BSS To derive our nonlinear BSS algorithm, we first present a brief review of higher-order cumulants-based linear BSS methods.  ... 
doi:10.1007/s10994-005-1506-8 fatcat:tbpq7edwhncc5hdips42h2mevq

Image denoising using self-organizing map-based nonlinear independent component analysis

Michel Haritopoulos, Hujun Yin, Nigel M. Allinson
2002 Neural Networks  
We then detail a BSS method based on SOMs and intended for image denoising applications.  ...  This paper proposes the use of self-organizing maps (SOMs) to the blind source separation (BSS) problem for nonlinearly mixed signals corrupted with multiplicative noise.  ...  A common assumption of linear ICA-based methods is the absence of noise and that the number of mixtures must, at least, equal the number of sources.  ... 
doi:10.1016/s0893-6080(02)00081-3 pmid:12416696 fatcat:t373dcy7jjbgbi3r737zoslm6i

Generalizing Independent Component Analysis for Two Related Data Sets

J. Karhunen, T. Ukkonen
2006 The 2006 IEEE International Joint Conference on Neural Network Proceedings  
We introduce in this paper methods for finding mutually corresponding dependent components from two different but related data sets in an unsupervised (blind) manner.  ...  We present experimental results demonstrating the usefulness of the proposed methods both for artificially generated data and for a cryptographic problem.  ...  In ICA and blind source separation (BSS) [17] , [4] , measures of statistical dependence have been developed and studied in several papers.  ... 
doi:10.1109/ijcnn.2006.246772 dblp:conf/ijcnn/KarhunenU06 fatcat:glik7tmcfjesfcqoi6nqeqp7kq

Extending ICA for finding jointly dependent components from two related data sets

Juha Karhunen, Tomas Ukkonen
2007 Neurocomputing  
In this paper, we introduce some methods for finding mutually corresponding dependent components from two different but related data sets in an unsupervised (blind) manner.  ...  We present experimental results demonstrating the usefulness of the proposed methods both for artificially generated data and for a cryptographic problem. r 2006 Published by Elsevier B.V. J.  ...  We can try to roughly diagonalize all these matrices by diagonalizing just their sum matrix Efxy T þ xgðyÞ T þ gðxÞy T g. (13) In this respect, our method resembles ICA and blind source separation (BSS  ... 
doi:10.1016/j.neucom.2006.10.144 fatcat:qqtmqx7z4ng3zbgw4pvjkzeqbu
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