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Relevant bibliographies by topics / Rank-1 approximation

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Academic literature on the topic 'Rank-1 approximation'

Author: Grafiati

Published: 4 June 2021

Last updated: 9 February 2022

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Journal articles on the topic "Rank-1 approximation"

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Kroo, Andras. "Chebyshev Rank in L 1 -Approximation." Transactions of the American Mathematical Society 296, no. 1 (1986): 301. http://dx.doi.org/10.2307/2000575.

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Stegeman, Alwin, and Pierre Comon. "Subtracting a best rank-1 approximation may increase tensor rank." Linear Algebra and its Applications 433, no. 7 (2010): 1276–300. http://dx.doi.org/10.1016/j.laa.2010.06.027.

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Kro{ó, Andr{ás. "Chebyshev rank in $L\sb 1$-approximation." Transactions of the American Mathematical Society 296, no. 1 (1986): 301. http://dx.doi.org/10.1090/s0002-9947-1986-0837813-5.

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Nasdala, Robert, and Daniel Potts. "Transformed rank-1 lattices for high-dimensional approximation." ETNA - Electronic Transactions on Numerical Analysis 53 (2020): 239–82. http://dx.doi.org/10.1553/etna_vol53s239.

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Bossmann, Florian, and Jianwei Ma. "Enhanced image approximation using shifted rank-1 reconstruction." Inverse Problems & Imaging 14, no. 2 (2020): 267–90. http://dx.doi.org/10.3934/ipi.2020012.

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Wu, Leqin, Xin Liu, and Zaiwen Wen. "Symmetric rank-1 approximation of symmetric high-order tensors." Optimization Methods and Software 35, no. 2 (2019): 416–38. http://dx.doi.org/10.1080/10556788.2019.1678034.

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Bendazzoli, Gian Luigi. "Rank-1 approximation to the van der Waals interaction." Theoretical Chemistry Accounts 118, no. 1 (2007): 135–42. http://dx.doi.org/10.1007/s00214-007-0256-z.

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Kuo, Frances Y., Giovanni Migliorati, Fabio Nobile, and Dirk Nuyens. "Function integration, reconstruction and approximation using rank-$1$ lattices." Mathematics of Computation 90, no. 330 (2021): 1861–97. http://dx.doi.org/10.1090/mcom/3595.

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Curtef, O., G. Dirr, and U. Helmke. "Conjugate gradient algorithms for best rank-1 approximation of tensors." PAMM 7, no. 1 (2007): 1062201–2. http://dx.doi.org/10.1002/pamm.200700706.

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Wang, Yiju, Manman Dong, and Yi Xu. "A sparse rank-1 approximation algorithm for high-order tensors." Applied Mathematics Letters 102 (April 2020): 106140. http://dx.doi.org/10.1016/j.aml.2019.106140.

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Dissertations / Theses on the topic "Rank-1 approximation"

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Volkmer, Toni. "Multivariate Approximation and High-Dimensional Sparse FFT Based on Rank-1 Lattice Sampling." Doctoral thesis, Universitätsbibliothek Chemnitz, 2017. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-222820.

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In this work, the fast evaluation and reconstruction of multivariate trigonometric polynomials with frequencies supported on arbitrary index sets of finite cardinality is considered, where rank-1 lattices are used as spatial discretizations. The approximation of multivariate smooth periodic functions by trigonometric polynomials is studied, based on a one-dimensional FFT applied to function samples. The smoothness of the functions is characterized via the decay of their Fourier coefficients, and various estimates for sampling errors are shown, complemented by numerical tests for up to 25 dimen

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Kämmerer, Lutz. "High Dimensional Fast Fourier Transform Based on Rank-1 Lattice Sampling." Doctoral thesis, Universitätsbibliothek Chemnitz, 2015. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-157673.

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We consider multivariate trigonometric polynomials with frequencies supported on a fixed but arbitrary frequency index set I, which is a finite set of integer vectors of length d. Naturally, one is interested in spatial discretizations in the d-dimensional torus such that - the sampling values of the trigonometric polynomial at the nodes of this spatial discretization uniquely determines the trigonometric polynomial, - the corresponding discrete Fourier transform is fast realizable, and - the corresponding fast Fourier transform is stable. An algorithm that computes the discrete Fourier trans

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Kämmerer, Lutz. "High Dimensional Fast Fourier Transform Based on Rank-1 Lattice Sampling." Doctoral thesis, Universitätsverlag der Technischen Universität Chemnitz, 2014. https://monarch.qucosa.de/id/qucosa%3A20167.

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We consider multivariate trigonometric polynomials with frequencies supported on a fixed but arbitrary frequency index set I, which is a finite set of integer vectors of length d. Naturally, one is interested in spatial discretizations in the d-dimensional torus such that - the sampling values of the trigonometric polynomial at the nodes of this spatial discretization uniquely determines the trigonometric polynomial, - the corresponding discrete Fourier transform is fast realizable, and - the corresponding fast Fourier transform is stable. An algorithm that computes the discrete Fourier trans

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Silva, Alex Pereira da. "Techniques tensorielles pour le traitement du signal : algorithmes pour la décomposition polyadique canonique." Thesis, Université Grenoble Alpes (ComUE), 2016. http://www.theses.fr/2016GREAT042/document.

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L’approximation tensorielle de rang faible joue ces dernières années un rôle importantdans plusieurs applications, telles que la séparation aveugle de source, les télécommunications, letraitement d’antennes, les neurosciences, la chimiométrie, et l’exploration de données. La décompositiontensorielle Canonique Polyadique est très attractive comparativement à des outils matriciels classiques,notamment pour l’identification de systèmes. Dans cette thèse, nous proposons (i) plusieursalgorithmes pour calculer quelques approximations de rang faible spécifique: approximation de rang-1 itérative et en

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Volkmer, Toni [Verfasser], Daniel [Akademischer Betreuer] Potts, Daniel [Gutachter] Potts, Gerlind [Gutachter] Plonka-Hoch, and Dirk [Gutachter] Pflüger. "Multivariate Approximation and High-Dimensional Sparse FFT Based on Rank-1 Lattice Sampling / Toni Volkmer ; Gutachter: Daniel Potts, Gerlind Plonka-Hoch, Dirk Pflüger ; Betreuer: Daniel Potts." Chemnitz : Universitätsbibliothek Chemnitz, 2017. http://d-nb.info/1214377459/34.

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Plan, Yaniv. "Compressed Sensing, Sparse Approximation, and Low-Rank Matrix Estimation." Thesis, 2011. https://thesis.library.caltech.edu/6259/1/thesis.pdf.

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<p>The importance of sparse signal structures has been recognized in a plethora of applications ranging from medical imaging to group disease testing to radar technology. It has been shown in practice that various signals of interest may be (approximately) sparsely modeled, and that sparse modeling is often beneficial, or even indispensable to signal recovery. Alongside an increase in applications, a rich theory of sparse and compressible signal recovery has recently been developed under the names compressed sensing (CS) and sparse approximation (SA). This revolutionary research has demonst

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Zeng, Wenjun. "Robust Low-Rank Approximation of Matrices in lp-Space." Phd thesis, 2018. https://tuprints.ulb.tu-darmstadt.de/7564/1/2018-07-05_Zeng_Wenjun.pdf.

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Low-rank approximation plays an important role in many areas of science and engineering such as signal/image processing, machine learning, data mining, imaging, bioinformatics, pattern classification and computer vision because many real-world data exhibit low-rank property. This dissertation devises advanced algorithms for robust low-rank approximation of a single matrix as well as multiple matrices in the presence of outliers, where the conventional dimensionality reduction techniques such as the celebrated principal component analysis (PCA) are not applicable. The proposed methodology is ba

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Pototskaia, Vlada. "Application of AAK theory for sparse approximation." Doctoral thesis, 2017. http://hdl.handle.net/11858/00-1735-0000-0023-3F4B-1.

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Books on the topic "Rank-1 approximation"

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Markovsky, Ivan. Low Rank Approximation. Springer London, 2012. http://dx.doi.org/10.1007/978-1-4471-2227-2.

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Book chapters on the topic "Rank-1 approximation"

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Jaiswal, Ragesh, and Amit Kumar. "Multiplicative Rank-1 Approximation using Length-Squared Sampling." In Symposium on Simplicity in Algorithms. Society for Industrial and Applied Mathematics, 2020. http://dx.doi.org/10.1137/1.9781611976014.4.

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Chu, Peng, Yu Pang, Erkang Cheng, Ying Zhu, Yefeng Zheng, and Haibin Ling. "Structure-Aware Rank-1 Tensor Approximation for Curvilinear Structure Tracking Using Learned Hierarchical Features." In Medical Image Computing and Computer-Assisted Intervention – MICCAI 2016. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-46720-7_48.

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Dewilde, Patrick, and Alle-Jan van der Veen. "Low-Rank Matrix Approximation and Subspace Tracking." In Time-Varying Systems and Computations. Springer US, 1998. http://dx.doi.org/10.1007/978-1-4757-2817-0_11.

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Janecek, Andreas, and Ying Tan. "Swarm Intelligence for Dimensionality Reduction." In Emerging Research on Swarm Intelligence and Algorithm Optimization. IGI Global, 2015. http://dx.doi.org/10.4018/978-1-4666-6328-2.ch013.

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Low-rank approximations allow for compact representations of data with reduced storage and runtime requirements and reduced redundancy and noise. The Non-Negative Matrix Factorization (NMF) is a special low-rank approximation that allows for additive parts-based, interpretable representation of the data. Various properties of NMF are similar to Swarm Intelligence (SI) methods: indeed, most NMF objective functions and most SI fitness functions are non-convex, discontinuous, and may possess many local minima. This chapter summarizes efforts on improving convergence, approximation quality, and classification accuracy of NMF using five different meta-heuristics based on SI and evolutionary computation. The authors present (1) new initialization strategies for NMF, and (2) an iterative update strategy for NMF. The applicability of the approach is illustrated on data sets coming from the areas of spam filtering and email classification. Experimental results show that both optimization strategies are able to improve NMF in terms of faster convergence, lower approximation error, and/or better classification accuracy.

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Sutton, Adrian P. "Strain." In Physics of Elasticity and Crystal Defects. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198860785.003.0001.

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A discussion of the continuum approximation is followed by the definition of deformation as a transformation involving changes in separation between points within a continuum. This leads to the mathematical definition of the deformation tensor. The introduction of the displacement vector and its gradient leads to the definition of the strain tensor. The linear elastic strain tensor involves an approximation in which gradients of the displacement vector are assumed to be small. The deformation tensor can be written as the sum of syymetric and antisymmetric parts, the former being the strain tensor. Normal and shear strains are distinguished. Problems set 1 introduces the strain ellipsoid, the invariance of the trace of the strain tensor, proof that the strain tensor satisfies the transformation law of second rank tensors and a general expression for the change in separation of points within a continuum subjected to a homogeneous strain.

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Reutenauer, Christophe. "Markoff’s Theorem for Approximations." In From Christoffel Words to Markoff Numbers. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198827542.003.0009.

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This chapter provesMarkoff’s theorem for approximations: if x is an irrational real number such that its Lagrange number L(x) is <3, then the continued fraction of x is ultimately periodic and has as periodic pattern a Christoffel word written on the alphabet 11, 22. Moreover, the bound is attained: this means that there are indeed convergents whose error terms are correctly bounded. For this latter result, one needs a lot of technical results, which use the notion of good and bad approximation of a real number x satisfying L(x) <3: the ranks of the good and bad convergents are precisely given. These results are illustrated by the golden ratio and the number 1 + square root of 2.

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Ruotsalo, Tuukka, and Eetu Mäkelä. "A Comparison of Corpus-Based and Structural Methods on Approximation of Semantic Relatedness in Ontologies." In Semantic Services, Interoperability and Web Applications. IGI Global, 2011. http://dx.doi.org/10.4018/978-1-60960-593-3.ch014.

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In this paper, the authors compare the performance of corpus-based and structural approaches to determine semantic relatedness in ontologies. A large light-weight ontology and a news corpus are used as materials. The results show that structural measures proposed by Wu and Palmer, and Leacock and Chodorow have superior performance when cut-off values are used. The corpus-based method Latent Semantic Analysis is found more accurate on specific rank levels. In further investigation, the approximation of structural measures and Latent Semantic Analysis show a low level of overlap and the methods are found to approximate different types of relations. The results suggest that a combination of corpus-based methods and structural methods should be used and appropriate cut-off values should be selected according to the intended use case.

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Janecek, Andreas, and Ying Tan. "Swarm Intelligence for Non-Negative Matrix Factorization." In Recent Algorithms and Applications in Swarm Intelligence Research. IGI Global, 2013. http://dx.doi.org/10.4018/978-1-4666-2479-5.ch009.

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The Non-negative Matrix Factorization (NMF) is a special low-rank approximation which allows for an additive parts-based and interpretable representation of the data. This article presents efforts to improve the convergence, approximation quality, and classification accuracy of NMF using five different meta-heuristics based on swarm intelligence. Several properties of the NMF objective function motivate the utilization of meta-heuristics: this function is non-convex, discontinuous, and may possess many local minima. The proposed optimization strategies are two-fold: On the one hand, a new initialization strategy for NMF is presented in order to initialize the NMF factors prior to the factorization; on the other hand, an iterative update strategy is proposed, which improves the accuracy per runtime for the multiplicative update NMF algorithm. The success of the proposed optimization strategies are shown by applying them on synthetic data and data sets coming from the areas of spam filtering/email classification, and evaluate them also in their application context. Experimental results show that both optimization strategies are able to improve NMF in terms of faster convergence, lower approximation error, and better classification accuracy. Especially the initialization strategy leads to significant reductions of the runtime per accuracy ratio for both, the NMF approximation as well as the classification results achieved with NMF.

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Bayraktar, Nihal, Tuan Minh Le, and Blanca Moreno-Dodson. "Tax Revenues and Tax Efforts across the World." In Handbook of Research on Public Finance in Europe and the MENA Region. IGI Global, 2016. http://dx.doi.org/10.4018/978-1-5225-0053-7.ch004.

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This chapter focuses on the concept and empirical estimation of tax effort around the world. It employs a cross-country study from a sample of 121, developing and developed countries during 1994-2012. Predicted tax revenue of a country is estimated empirically taking into account its specific economic, demographic, and institutional features and is considered as an approximation of its taxable capacity. Tax effort is then defined as the ratio between the share of the actual tax collection and the predicted tax revenue. The use of tax effort and actual tax revenue collection allows us to rank countries into four different groups. The results vary per country and region but, overall, tax revenue collection appears to be in line with its predicted value. This could reflect many efforts undertaken in the last decades to improve tax policy and tax administration. It also suggests that further improvements in domestic revenue mobilization may require other non-tax reforms aimed at removing economic, demographic and institutional constraints hindering tax revenue performance.

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Conference papers on the topic "Rank-1 approximation"

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Shi, Xinchu, Haibin Ling, Junliang Xing, and Weiming Hu. "Multi-target Tracking by Rank-1 Tensor Approximation." In 2013 IEEE Conference on Computer Vision and Pattern Recognition (CVPR). IEEE, 2013. http://dx.doi.org/10.1109/cvpr.2013.309.

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Song, Zhao, David P. Woodruff, and Peilin Zhong. "Low rank approximation with entrywise l 1 -norm error." In STOC '17: Symposium on Theory of Computing. ACM, 2017. http://dx.doi.org/10.1145/3055399.3055431.

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Chuan Sun, Imran Junejo, and Hassan Foroosh. "Action recognition using rank-1 approximation of Joint Self-Similarity Volume." In 2011 IEEE International Conference on Computer Vision (ICCV). IEEE, 2011. http://dx.doi.org/10.1109/iccv.2011.6126345.

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Serizel, Romain, Marc Moonen, Bas Van Dijk, and Jan Wouters. "Rank-1 approximation based multichannel wiener filtering algorithms for noise reduction in cochlear implants." In ICASSP 2013 - 2013 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2013. http://dx.doi.org/10.1109/icassp.2013.6639351.

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Aissa-El-Bey, Abdeldjalil, and Abd-Krim Seghouane. "Sparse canonical correlation analysis based on rank-1 matrix approximation and its application for FMRI signals." In 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2016. http://dx.doi.org/10.1109/icassp.2016.7472564.

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Iqbal, Asif, and Abd-Krim Seghouane. "An Algorithm for Multi Subject Fmri Analysis Based on the SVD and Penalized Rank-1 Matrix Approximation." In ICASSP 2018 - 2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2018. http://dx.doi.org/10.1109/icassp.2018.8461728.

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Yaguchi, Atsushi, Taiji Suzuki, Shuhei Nitta, Yukinobu Sakata, and Akiyuki Tanizawa. "Decomposable-Net: Scalable Low-Rank Compression for Neural Networks." In Thirtieth International Joint Conference on Artificial Intelligence {IJCAI-21}. International Joint Conferences on Artificial Intelligence Organization, 2021. http://dx.doi.org/10.24963/ijcai.2021/447.

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Compressing DNNs is important for the real-world applications operating on resource-constrained devices. However, we typically observe drastic performance deterioration when changing model size after training is completed. Therefore, retraining is required to resume the performance of the compressed models suitable for different devices. In this paper, we propose Decomposable-Net (the network decomposable in any size), which allows flexible changes to model size without retraining. We decompose weight matrices in the DNNs via singular value decomposition and adjust ranks according to the targe

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Cui, Wanyun, and Sen Yan. "Isotonic Data Augmentation for Knowledge Distillation." In Thirtieth International Joint Conference on Artificial Intelligence {IJCAI-21}. International Joint Conferences on Artificial Intelligence Organization, 2021. http://dx.doi.org/10.24963/ijcai.2021/319.

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Knowledge distillation uses both real hard labels and soft labels predicted by teacher model as supervision. Intuitively, we expect the soft label probabilities and hard label probabilities to be concordant. However, in the real knowledge distillations, we found critical rank violations between hard labels and soft labels for augmented samples. For example, for an augmented sample x = 0.7 * cat + 0.3 * panda, a meaningful soft label distribution should have the same rank: P(cat|x)>P(panda|x)>P(other|x). But real teacher models usually violate the rank: P(tiger|x)>P(panda|x)>P(cat|x

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Comon, Pierre, and Mikael Sorensen. "Decomposing tensors with structured matrix factors reduces to rank-1 approximations." In 2010 IEEE International Conference on Acoustics, Speech and Signal Processing. IEEE, 2010. http://dx.doi.org/10.1109/icassp.2010.5495816.

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Zeinalzadeh, Ashkan, Tom Wenska, and Gordon Okimoto. "Integrated analysis of multiple high-dimensional data sets by joint rank-1 matrix approximations." In 2015 54th IEEE Conference on Decision and Control (CDC). IEEE, 2015. http://dx.doi.org/10.1109/cdc.2015.7402818.

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