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Constrained Projection Approximation Algorithms for Principal Component Analysis

Seungjin Choi, Jong-Hoon Ahn, Andrzej Cichocki
2006 Neural Processing Letters  
Then, we present iterative algorithms for the IRE minimization, where we use the projection approximation.  ...  The proposed algorithm is referred to as COnstrained Projection Approximation (COPA) algorithm and its limiting case is called COPAL.  ...  Introduction Principal component analysis (PCA) or principal subspace analysis (PSA) is a fundamental multivariate data analysis method which is encountered into a variety of areas in neural networks,  ... 
doi:10.1007/s11063-006-9011-z fatcat:5bjvsqby4bgtpflwytxensqdy4

Principal Component Analysis Applied to Gradient Fields in Band Gap Optimization Problems for Metamaterials [article]

Giorgio Gnecco, Andrea Bacigalupo, Francesca Fantoni, Daniela Selvi
2021 arXiv   pre-print
In this framework, the present article describes the application of a related unsupervised machine learning technique, namely, principal component analysis, to approximate the gradient of the objective  ...  A promising technique for the spectral design of acoustic metamaterials is based on the formulation of suitable constrained nonlinear optimization problems.  ...  for the number p of principal components kept .  ... 
arXiv:2104.02588v6 fatcat:rcqyxlwdovg2tl6rx74kemw4ci

Principal graphs and piecewise linear subspace constrained mean-shift

Umut Ozertem, Deniz Erdogmus
2008 2008 IEEE Workshop on Machine Learning for Signal Processing  
One of the important problems with most existing principal curve algorithms is that they are seeking for a smooth curve.  ...  We propose a nonparametric principal graph algorithm, and apply it to optical character recognition, where handling the above mentioned irregularities like loops and self-intersections is a serious problem  ...  The authors would like to thank Balazs Kegl for providing the optical character dataset. This work is partially funded by NSF grants ECS-0524835, and ECS-0622239.  ... 
doi:10.1109/mlsp.2008.4685520 fatcat:uogefpktxrekla3375avkzjcsu

Information Projection and Approximate Inference for Structured Sparse Variables [article]

Rajiv Khanna, Joydeep Ghosh, Russell Poldrack, Oluwasanmi Koyejo
2016 arXiv   pre-print
This manuscript goes beyond classical sparsity by proposing efficient algorithms for approximate inference via information projection that are applicable to any structure on the set of variables that admits  ...  The class of probabilistic models that can be expressed in this way is quite broad and, as we show, includes group sparse regression, group sparse principal components analysis and sparse canonical correlation  ...  Subsequently, a similar mechanism was developed for sparse principal components analysis (sparse PCA) [8] .  ... 
arXiv:1607.03204v1 fatcat:3ho3fgvktzagva5rwxkxtmdaaq

Neural Network Implementations for PCA and Its Extensions

Jialin Qiu, Hui Wang, Jiabin Lu, Biaobiao Zhang, K.-L. Du
2012 ISRN Artificial Intelligence  
In this paper, we give an introduction to various neural network implementations and algorithms for principal component analysis (PCA) and its various extensions.  ...  Minor component analysis (MCA) is a variant of PCA, which is useful for solving total least squares (TLSs) problems. The algorithms are typical unsupervised learning methods.  ...  Constrained PCA, generalized EVD, and the two-dimensional PCA are three important generalizations to PCA. 12.1. Constrained Principal Component Analysis.  ... 
doi:10.5402/2012/847305 fatcat:5v5l5v56ozg7lkxfktm5t7cgle

A Literature Survey on High-Dimensional Sparse Principal Component Analysis

Shen Ning-min, Li Jing
2015 International Journal of Database Theory and Application  
Sparse principal component analysis (sparse PCA) is proposed mainly for the challenges of PCA above.  ...  Principal Component Analysis (PCA) is a classical method for dimensionality reduction, data pre-processing, compression and visualization of multivariate data for different applications in biology, social  ...  Acknowledgements This paper is partially supported by Fundamental Research Funds for the Central University (NS2015092).  ... 
doi:10.14257/ijdta.2015.8.6.06 fatcat:6nt3kqwtjzhiznqj2ylzmbjnbi

Boosting Constrained Mutual Subspace Method for Robust Image-Set Based Object Recognition

Xi Li, Kazuhiro Fukui, Nanning Zheng
2009 International Joint Conference on Artificial Intelligence  
Constrained Mutual Subspace Method (CMSM) is one of the state-of-the-art algorithms for imageset based object recognition by first projecting the image-set patterns onto the so-called generalized difference  ...  subspace then classifying based on the principal angle based mutual subspace distance.  ...  For each image-set instance X i j compute its corresponding subspace base U i j using principal component analysis.  ... 
dblp:conf/ijcai/LiFZ09 fatcat:cilpqw47xrenxheit7ghawpfgm

Smooth Signal Extraction From Instantaneous Mixtures

Nikolaos Mitianoudis, Tania Stathaki, Anthony G. Constantinides
2007 IEEE Signal Processing Letters  
The approach incorporates smoothness constraints in the traditional negentropy cost function to extract smooth components, using an approximate second-order optimization method.  ...  The problem of blind separation of statistically independent sources from instantaneous mixtures, using the efficient framework of independent component analysis (ICA), has been widely addressed in the  ...  ACKNOWLEDGMENT The authors would like to thank the reviewers for their insightful comments.  ... 
doi:10.1109/lsp.2006.885287 fatcat:4npw6fcoarg25bczl46kbmhp3a

Clustering Based on Principal Curve [chapter]

Ioan Cleju, Pasi Fränti, Xiaolin Wu
2005 Lecture Notes in Computer Science  
Clustering algorithms are intensively used in the image analysis field in compression, segmentation, recognition and other tasks.  ...  The algorithm heuristically prolongs the optimal scalar quantization technique to vector space. The data set is sequenced using one-dimensional projection spaces.  ...  Ioan Cleju's work is currently supported by DFG Graduiertenkolleg/1042 'Explorative Analysis and Visualization of Large Information Spaces' at University of Konstanz, Germany.  ... 
doi:10.1007/11499145_88 fatcat:zifxlelmizasbck67mtbfyqady

Expectation-maximization for sparse and non-negative PCA

Christian D. Sigg, Joachim M. Buhmann
2008 Proceedings of the 25th international conference on Machine learning - ICML '08  
This problem is known as sparse and non-negative principal component analysis (PCA), and has many applications including dimensionality reduction and feature selection.  ...  We demonstrate significant improvements in performance and computational efficiency compared to other constrained PCA algorithms, on large data sets from biology and computer vision.  ...  Acknowledgements We thank Wolfgang Einhäuser-Treyer, Peter Orbanz and the anonymous reviewers for their valuable comments on the manuscript. This work was in part funded by CTI grant 8539.2;2 ESPP-ES.  ... 
doi:10.1145/1390156.1390277 dblp:conf/icml/SiggB08 fatcat:2hepxelr5fg7lj2rfinypmg6tu

Objective-Sensitive Principal Component Analysis for High-Dimensional Inverse Problems [article]

Maksim Elizarev, Andrei Mukhin, Aleksey Khlyupin
2020 arXiv   pre-print
The developed technique is based on principal component analysis (PCA) but modifies a purely data-driven basis of principal components considering objective function behavior.  ...  Three algorithms for optimal parameter decomposition are presented and applied to an objective of 2D synthetic history matching.  ...  Conclusion A novel algorithm for objective-sensitive principal component analysis of random fields was developed.  ... 
arXiv:2006.04527v1 fatcat:p5uu4viuqjhbvkp7jemjoh4nma

Principal Curves as Skeletons of Tubular Objects

Erhan Bas, Deniz Erdogmus
2011 Neuroinformatics  
Then, given an initial direction and location, the algorithm iteratively traces the principal curve in space using our principal curve tracing (PCT) method.  ...  Developments in image acquisition technology make high volumes of neuron images available to neuroscientists for analysis.  ...  Acknowledgements The authors would like to thank the organizers and data providers of the Diadem Challenge for putting together this challenge.  ... 
doi:10.1007/s12021-011-9105-2 pmid:21336847 fatcat:uxc5cmki4ngwhk2qwjt7i7ltmy

Characterizing Variability of Modular Brain Connectivity with Constrained Principal Component Analysis

Jun-ichiro Hirayama, Aapo Hyvärinen, Vesa Kiviniemi, Motoaki Kawanabe, Okito Yamashita, Satoru Hayasaka
2016 PLoS ONE  
Principal component analysis (PCA) serves as a fundamental statistical technique for such analyses.  ...  OPEN ACCESS Citation: Hirayama J-i, Hyvärinen A, Kiviniemi V, Kawanabe M, Yamashita O (2016) Characterizing Variability of Modular Brain Connectivity with Constrained Principal Component Analysis.  ...  Acknowledgments We gratefully thank Masa-aki Sato and Mitsuo Kawato for helpful comments and Takashi Yamada, Masahiro Yamashita, and Ayumu Yamashita for information on existing fcMRI studies.  ... 
doi:10.1371/journal.pone.0168180 pmid:28002474 pmcid:PMC5176286 fatcat:5z2ijvcip5eshg4jmg4s6kjwnm

Reduced-order constrained optimization in IMRT planning

Renzhi Lu, Richard J Radke, Jie Yang, Laura Happersett, Ellen Yorke, Andrew Jackson
2008 Physics in Medicine and Biology  
Next, we apply principal component analysis (PCA) to this set of plans, revealing that the high-dimensional intensity space can be spanned by only a few basis vectors.  ...  based on an approximate dose calculation algorithm.  ...  Acknowledgments This work was supported by the National Cancer Institute under grant 5P01CA59017-13, and CenSSIS, the NSF Center for Subsurface Sensing and Imaging Systems, under the award EEC-9986821.  ... 
doi:10.1088/0031-9155/53/23/007 pmid:18997270 pmcid:PMC2907243 fatcat:5littjxqnzdgdpmpsdpq5h2zaa

Reduced-order Constrained Optimization in IMRT Planning

R. Lu, R. Radke, L. Happersett, J. Yang, E. Yorke, A. Jackson
2008 International Journal of Radiation Oncology, Biology, Physics  
Next, we apply principal component analysis (PCA) to this set of plans, revealing that the high-dimensional intensity space can be spanned by only a few basis vectors.  ...  based on an approximate dose calculation algorithm.  ...  Acknowledgments This work was supported by the National Cancer Institute under grant 5P01CA59017-13, and CenSSIS, the NSF Center for Subsurface Sensing and Imaging Systems, under the award EEC-9986821.  ... 
doi:10.1016/j.ijrobp.2008.06.962 fatcat:zo26atpixrc3xhheibm45ouhxa
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