Relevant bibliographies by topics / Rank-one tensors

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Rank-one tensors'

Author: Grafiati
Published: 10 March 2023

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Journal articles on the topic "Rank-one tensors"

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POPA, FLORIAN CATALIN, and OVIDIU TINTAREANU-MIRCEA. "IRREDUCIBLE KILLING TENSORS FROM THIRD RANK KILLING–YANO TENSORS." Modern Physics Letters A 22, no. 18 (2007): 1309–17. http://dx.doi.org/10.1142/s0217732307023559.

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We investigate higher rank Killing–Yano tensors showing that third rank Killing–Yano tensors are not always trivial objects being possible to construct irreducible Killing tensors from them. We give as an example the Kimura IIC metric from two-rank Killing–Yano tensors to obtain a reducible Killing tensor and from third-rank Killing–Yano tensors, we obtain three Killing tensors, one reducible and two irreducible.
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Tyrtyshnikov, Eugene E. "Tensor decompositions and rank increment conjecture." Russian Journal of Numerical Analysis and Mathematical Modelling 35, no. 4 (2020): 239–46. http://dx.doi.org/10.1515/rnam-2020-0020.

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AbstractSome properties of tensor ranks and the non-closeness issue of sets with given restrictions on the rank of tensors entering those sets are studied. It is proved that the rank of the d-dimensional Laplacian equals d. The following conjecture is formulated: for any tensor of non-maximal rank there exists a nonzero decomposable tensor (tensor of rank 1) such that the rank increases by one after adding this tensor. In the general case, it is proved that this property holds algebraically almost everywhere for complex tensors of fixed size whose rank is strictly less than the generic rank.
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Zhang, Tong, and Gene H. Golub. "Rank-One Approximation to High Order Tensors." SIAM Journal on Matrix Analysis and Applications 23, no. 2 (2001): 534–50. http://dx.doi.org/10.1137/s0895479899352045.

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Hu, Shenglong, Defeng Sun, and Kim-Chuan Toh. "Best Nonnegative Rank-One Approximations of Tensors." SIAM Journal on Matrix Analysis and Applications 40, no. 4 (2019): 1527–54. http://dx.doi.org/10.1137/18m1224064.

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Bachmayr, Markus, Wolfgang Dahmen, Ronald DeVore, and Lars Grasedyck. "Approximation of High-Dimensional Rank One Tensors." Constructive Approximation 39, no. 2 (2013): 385–95. http://dx.doi.org/10.1007/s00365-013-9219-x.

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Friedland, S., V. Mehrmann, R. Pajarola, and S. K. Suter. "On best rank one approximation of tensors." Numerical Linear Algebra with Applications 20, no. 6 (2013): 942–55. http://dx.doi.org/10.1002/nla.1878.

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Breiding, Paul, and Nick Vannieuwenhoven. "On the average condition number of tensor rank decompositions." IMA Journal of Numerical Analysis 40, no. 3 (2019): 1908–36. http://dx.doi.org/10.1093/imanum/drz026.

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Abstract We compute the expected value of powers of the geometric condition number of random tensor rank decompositions. It is shown in particular that the expected value of the condition number of $n_1\times n_2 \times 2$ tensors with a random rank-$r$ decomposition, given by factor matrices with independent and identically distributed standard normal entries, is infinite. This entails that it is expected and probable that such a rank-$r$ decomposition is sensitive to perturbations of the tensor. Moreover, it provides concrete further evidence that tensor decomposition can be a challenging pr
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Grasedyck, Lars, and Wolfgang Hackbusch. "An Introduction to Hierarchical (H-) Rank and TT-Rank of Tensors with Examples." Computational Methods in Applied Mathematics 11, no. 3 (2011): 291–304. http://dx.doi.org/10.2478/cmam-2011-0016.

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Abstract We review two similar concepts of hierarchical rank of tensors (which extend the matrix rank to higher order tensors): the TT-rank and the H-rank (hierarchical or H-Tucker rank). Based on this notion of rank, one can define a data-sparse representation of tensors involving O(dnk + dk^3) data for order d tensors with mode sizes n and rank k. Simple examples underline the differences and similarities between the different formats and ranks. Finally, we derive rank bounds for tensors in one of the formats based on the ranks in the other format.
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Krieg, David, and Daniel Rudolf. "Recovery algorithms for high-dimensional rank one tensors." Journal of Approximation Theory 237 (January 2019): 17–29. http://dx.doi.org/10.1016/j.jat.2018.08.002.

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Milošević, Ivanka. "Second-rank tensors for quasi-one-dimensional systems." Physics Letters A 204, no. 1 (1995): 63–66. http://dx.doi.org/10.1016/0375-9601(95)00412-v.

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Dissertations / Theses on the topic "Rank-one tensors"

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Wang, Roy Chih Chung. "Adaptive Kernel Functions and Optimization Over a Space of Rank-One Decompositions." Thesis, Université d'Ottawa / University of Ottawa, 2017. http://hdl.handle.net/10393/36975.

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The representer theorem from the reproducing kernel Hilbert space theory is the origin of many kernel-based machine learning and signal modelling techniques that are popular today. Most kernel functions used in practical applications behave in a homogeneous manner across the domain of the signal of interest, and they are called stationary kernels. One open problem in the literature is the specification of a non-stationary kernel that is computationally tractable. Some recent works solve large-scale optimization problems to obtain such kernels, and they often suffer from non-identifiability iss
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Morgan, William Russell IV. "Investigations into Parallelizing Rank-One Tensor Decompositions." Thesis, University of Maryland, Baltimore County, 2018. http://pqdtopen.proquest.com/#viewpdf?dispub=10683240.

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<p> Tensor Decompositions are a solved problem in terms of evaluating for a result. Performance, however, is not. There are several projects to parallelize tensor decompositions, using a variety of different methods. This work focuses on investigating other possible strategies for parallelization of rank-one tensor decompositions, measuring performance across a variety of tensor sizes, and reporting the best avenues to continue investigation</p><p>
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Sokal, Bruno. "Semi-blind receivers for multi-relaying mimo systems using rank-one tensor factorizations." reponame:Repositório Institucional da UFC, 2017. http://www.repositorio.ufc.br/handle/riufc/25988.

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SOKAL, B. Semi-blind receivers for multi-relaying mimo systems using rank-one tensor factorizations. 2017. 85 f. Dissertação (Mestrado em Engenharia de Teleinformática)-Centro de Tecnologia, Universidade Federal do Ceará, Fortaleza, 2017.<br>Submitted by Renato Vasconcelos (ppgeti@ufc.br) on 2017-09-15T20:38:29Z No. of bitstreams: 1 2017_dis_bsokal.pdf: 1689224 bytes, checksum: f0e2e9424de721f23bf0629ba55330c1 (MD5)<br>Rejected by Marlene Sousa (mmarlene@ufc.br), reason: Prezado Bruno: Existe uma orientação para que normalizemos as dissertações e teses da UFC, em suas paginas pré-textuais e li
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Ossman, Hala. "Etude mathématique de la convergence de la PGD variationnelle dans certains espaces fonctionnels." Thesis, La Rochelle, 2017. http://www.theses.fr/2017LAROS006/document.

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On s’intéresse dans cette thèse à la PGD (Proper Generalized Decomposition), l’une des méthodes de réduction de modèles qui consiste à chercher, a priori, la solution d’une équation aux dérivées partielles sous forme de variables séparées. Ce travail est formé de cinq chapitres dans lesquels on vise à étendre la PGD aux espaces fractionnaires et aux espaces des fonctions à variation bornée, et à donner des interprétations théoriques de cette méthode pour une classe de problèmes elliptiques et paraboliques. Dans le premier chapitre, on fait un bref aperçu sur la littérature puis on présente les
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Sodomaco, Luca. "The Distance Function from the Variety of partially symmetric rank-one Tensors." Doctoral thesis, 2020. http://hdl.handle.net/2158/1220535.

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The topic of this doctoral thesis is at the intersection between Real Algebraic Geometry, Optimization Theory and Multilinear Algebra. In particular, a relevant part of this thesis is dedicated to studying metric invariants of real algebraic varieties, with a particular interest in varieties in tensor spaces. In many applications, tensors arise as a useful way to store and organize experimental data. For example, it is widely known that tensor techniques are extremely useful in Algebraic Statistics. A strong relationship between classical algebraic geometry and multilinear algebra is establis
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Book chapters on the topic "Rank-one tensors"

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Liu, Chang, Kun He, Ji-liu Zhou, and Chao-Bang Gao. "Discriminant Orthogonal Rank-One Tensor Projections for Face Recognition." In Intelligent Information and Database Systems. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-20042-7_21.

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Kobayashi, Toshiyuki, and Birgit Speh. "Minor Summation Formulæ Related to Exterior Tensor $$\begin{array}{lll}\bigwedge^i\;(\mathbb{C}^n)\end{array}$$." In Symmetry Breaking for Representations of Rank One Orthogonal Groups II. Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-13-2901-2_7.

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Kaimakamis, George, and Konstantina Panagiotidou. "The *-Ricci Tensor of Real Hypersurfaces in Symmetric Spaces of Rank One or Two." In Springer Proceedings in Mathematics & Statistics. Springer Japan, 2014. http://dx.doi.org/10.1007/978-4-431-55215-4_18.

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Oertel, Gerhard. "Effects of Stress." In Stress and Deformation. Oxford University Press, 1996. http://dx.doi.org/10.1093/oso/9780195095036.003.0011.

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The simplest relationship between stress and strain is Hooke’s law, describing the linear elastic response of solids to stress. Elastic strain (almost in all cases small) is proportional to the applied stress, with one proportionality factor expressing the relationship between normal, and another that between tangential stress and strain. An ideally elastic strain is completely reversed upon removal of the stress that has caused it. Most materials obey Hooke’s law somewhat imperfectly, and that only up to a critical yield stress beyond which they begin to flow and to acquire, in addition to the elastic strain, a permanent strain that does not revert upon stress release. Hooke’s law in this form is applied to materials that are elastically isotropic, or can be assumed to be approximately so. Crystals, however, never are elastically isotropic, nor are crystalline materials consisting of constituent grains with a distribution of crystallographic orientations that departs from being uniform. The response of a crystal to a stress (at a level below the yield stress) consists of a strain determined by a matter tensor of the fourth rank, the compliance tensor s i j k l : . . . ɛij = s i j k l σkl, (7.1) . . . the 81 components of which are constants. Any tensor that describes the linear relationship between two tensors of the second rank is necessarily of the fourth rank, and like other tensors of the fourth rank, the compliance tensor can be referred to a new set of reference coordinates by means of a rotation matrix aij: s i j k l = aimajnakoalp smnop. (7.2) . . . The components of the compliance tensor are highly redundant, first because both the stress and the strain tensors are symmetric, and second because the tensor itself is symmetric. The number of independent components for crystals of the lowest, triclinic (both classes) symmetry is 21, and with increasing crystal symmetry the redundancies become more numerous; only three independent compliances are needed to describe the elastic properties of a cubic crystal.
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Ting, T. T. C. "Transformation of the Elasticity Matrices and Dual Coordinate Systems." In Anisotropic Elasticity. Oxford University Press, 1996. http://dx.doi.org/10.1093/oso/9780195074475.003.0010.

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When the elasticity matrices are referred to a rotated coordinate system their elements change and assume different values. We will show in this chapter that, under rotations about the x3-axis, the matrices A and B are tensors of rank one while S, H, L, and M are tensors of rank two. These properties are important in establishing certain invariants that are physically interesting and puzzling. We will also present the amazing Barnett-Lothe integral formalism that allows us to determine S, H, and L without computing the eigenvalues and eigenvectors of elastic constants. New tensors Ni(θ) (i=l,2,3), S(θ), H(θ), L(θ), and Gi(θ) (i=1,3) are introduced, and their properties as well as identities relating them are presented. Also introduced is the idea of dual coordinate systems where the position of a point is referred to one coordinate system while the displacement components are referred to another coordinate system. These will be useful in applications. As in Chapter 6 readers may skip this chapter in the first reading. They can return to this chapter later for specific information.
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Ting, T. T. C. "The Structures and Identities of the Elasticity Matrices." In Anisotropic Elasticity. Oxford University Press, 1996. http://dx.doi.org/10.1093/oso/9780195074475.003.0009.

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The matrices Q, R, T, A, B, N1, N2, N3, S, H, L, and M introduced in the previous chapter are the elasticity matrices. They depend on elastic constants only, and appear frequently in the solutions to two-dimensional problems. The matrices A, B, and M are complex while the others are real. We present their structures and identities relating them in this chapter. In Chapter 7 we will show that A and B are tensors of rank one and S, H, L, and M are tensors of rank two when the transformation is a rotation about the x3-axis. Readers who are not interested in how the structures of these matrices and the identities relating them are derived may skip this chapter. They may return to this chapter when they read later chapters on applications where the results presented here are employed.
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Deng, Zhaoxian, and Zhiqiang Zeng. "Multi-View Subspace Clustering by Combining ℓ2,p-Norm and Multi-Rank Minimization of Tensors." In Frontiers in Artificial Intelligence and Applications. IOS Press, 2022. http://dx.doi.org/10.3233/faia220020.

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In this article, based on the self-represented multi-view subspace clustering framework, we propose a new clustering model. Based on the assumption that different features can be linearly represented by data mapped to different subspaces, multiview subspace learning methods take advantage of the complementary and consensus informations between various kind of views of the data can boost the clustering performance. We search for the tensor with the lowest rank and then extract the frontal slice of it to establish a well-structured affinity matrix. Based on the tensor singular value decomposition (t-SVD), our low-rank constraint can be achieved. We impose the ℓ2,p-norm to flexibly control the sparsity of the error matrix, making it more robust to noise, which will enhance the robustness of our clustering model. With combining ℓ2,p-norm and tensor multi-rank minimization, the proposed Multi-view Subspace Clustering(MVSC) model can effectively perform clustering with multiple data resources. We test our model on one real-world spoon dataset and several publicly availabe datasets. Extensive evaluation methods have proved that our model is effective and efficient.
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Green, Mark, Phillip Griffiths, and Matt Kerr. "Classification of Mumford-Tate Subdomains." In Mumford-Tate Groups and Domains. Princeton University Press, 2012. http://dx.doi.org/10.23943/princeton/9780691154244.003.0008.

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This chapter develops an algorithm for determining all Mumford-Tate subdomains of a given period domain. The result is applied to the classification of all complex multiplication Hodge structures (CM Hodge structures) of rank 4 and when the weight n = 1 and n = 3, to an analysis of their Hodge tensors and endomorphism algebras, and the number of components of the Noether-Lefschetz locus. The result is that one has a complex but very rich arithmetic story. Of particular note is the intricate structure of the components of the Noether-Lefschetz loci in D and in its compact dual, and the two interesting cases where the Hodge tensors are generated in degrees 2 and 4. One application is that a particular class of period maps appearing in mirror symmetry never has image in a proper subdomain of D.
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Newnham, Robert E. "Thermodynamic relationships." In Properties of Materials. Oxford University Press, 2004. http://dx.doi.org/10.1093/oso/9780198520757.003.0008.

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In the next few chapters we shall discuss tensors of rank zero to four which relate the intensive variables in the outer triangle of the Heckmann Diagram to the extensive variables in the inner triangle. Effects such as pyroelectricity, permittivity, pyroelectricity, and elasticity are the standard topics in crystal physics that allow us to discuss tensors of rank one through four. First, however, it is useful to introduce the thermodynamic relationships between physical properties and consider the importance of measurement conditions. Before discussing all the cross-coupled relationships, we first define the coupling within the three individual systems. In a thermal system, the basic relationship is between change in entropy δS [J/m3] and change in temperature δT [K]: . . . δS = CδT, . . . where C is the specific heat per unit volume [J/m3 K] and T is the absolute temperature. S, T, and C are all scalar quantities. In a dielectric system the electric displacement Di [C/m2] changes under the influence of the electric field Ei [V/m]. Both are vectors and therefore the electric permittivity, εij , requires two-directional subscripts. Occasionally the dielectric stiffness, βij , is required as well. . . . Di = εijEj Ei = βijDj. . . . Some authors use polarization P rather than electric displacement D. The three variables are interrelated through the constitutive relation . . . Di = Pi + ε0Ei = εijEj. . . . The third linear system in the Heckmann Diagram is mechanical, relating strain xij to stress Xkl [N/m2] through the fourth rank elastic compliance coefficients sijkl [m2/N]. . . . xij = sijklXkl. . . . Alternatively, Hooke’s Law can be expressed in terms of the elastic stiffness coefficients cijkl [N/m2]. . . Xij = cijklxkl. . . . When cross coupling occurs between thermal, electrical, and mechanical variables, the Gibbs free energy G(T, X, E) is used to derive relationships between the property coefficients. Temperature T, stress X, and electric field E are the independent variables in most experiments.
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Newnham, Robert E. "Diffusion and ionic conductivity." In Properties of Materials. Oxford University Press, 2004. http://dx.doi.org/10.1093/oso/9780198520757.003.0021.

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The phenomenon of atomic and ionic migration in crystals is called solidstate diffusion, and its study has shed light on many problems of technological and scientific importance. Diffusion is intimately connected to the strength of metals at high temperature, to metallurgical processes used to control alloy properties, and to many of the effects of radiation on nuclear reactor materials. Diffusion studies are important in understanding the ionic conductivity of the materials used in fuel cells, the fabrication of semiconductor integrated circuits, the corrosion of metals, and the sintering of ceramics. When two miscible materials are in contact across an interface, the quantity of diffusing material which passes through the interface is proportional to the concentration gradient. The atomic flux J is given by where J is measured per unit time and per unit area, c is the concentration of the diffusing material per unit volume, and Z is the gradient direction. The proportionality factor D, the diffusion coefficient, is measured in units of m2/s. This equation is sometimes referred to as Fick’s First Law. It describes atomic transport in a form that is analogous to electrical resistivity (Ohm’s Law) or thermal conductivity. There are several objections to Fick’s Law, as discussed in Section 19.5. Strictly speaking, it is valid only for self-diffusion coefficients measured in small concentration gradients. Since J and Z are both vectors, the diffusion coefficient D is a second rank tensor. As with other symmetric second rank tensors, between one and six measurements are required to specify Dij , depending on symmetry. The relationship between structure and anisotropy is more apparent in PbI2. Lead iodide is isostructural with CdI2 in trigonal point group.m. The self-diffusion of Pb is much easier parallel to the layers where the Pb atoms are in close proximity to one another. Diffusion is more difficult along Z3 = [001] because Pb atoms have a very long jump distance in this direction. The mineral olivine, (Mg, Fe)2SiO4, is an important constituent of the deeper parts of the earth’s crust.
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Conference papers on the topic "Rank-one tensors"

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Najafi, Mehrnaz, Lifang He, and Philip S. Yu. "Outlier-Robust Multi-Aspect Streaming Tensor Completion and Factorization." In Twenty-Eighth International Joint Conference on Artificial Intelligence {IJCAI-19}. International Joint Conferences on Artificial Intelligence Organization, 2019. http://dx.doi.org/10.24963/ijcai.2019/442.

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With the increasing popularity of streaming tensor data such as videos and audios, tensor factorization and completion have attracted much attention recently in this area. Existing work usually assume that streaming tensors only grow in one mode. However, in many real-world scenarios, tensors may grow in multiple modes (or dimensions), i.e., multi-aspect streaming tensors. Standard streaming methods cannot directly handle this type of data elegantly. Moreover, due to inevitable system errors, data may be contaminated by outliers, which cause significant deviations from real data values and mak
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Vora, Jian, Karthik S. Gurumoorthy, and Ajit Rajwade. "Recovery of Joint Probability Distribution from One-Way Marginals: Low Rank Tensors and Random Projections." In 2021 IEEE Statistical Signal Processing Workshop (SSP). IEEE, 2021. http://dx.doi.org/10.1109/ssp49050.2021.9513818.

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Yang, Chaoqi, Cheng Qian, and Jimeng Sun. "GOCPT: Generalized Online Canonical Polyadic Tensor Factorization and Completion." In Thirty-First International Joint Conference on Artificial Intelligence {IJCAI-22}. International Joint Conferences on Artificial Intelligence Organization, 2022. http://dx.doi.org/10.24963/ijcai.2022/326.

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Low-rank tensor factorization or completion is well-studied and applied in various online settings, such as online tensor factorization (where the temporal mode grows) and online tensor completion (where incomplete slices arrive gradually). However, in many real-world settings, tensors may have more complex evolving patterns: (i) one or more modes can grow; (ii) missing entries may be filled; (iii) existing tensor elements can change. Existing methods cannot support such complex scenarios. To fill the gap, this paper proposes a Generalized Online Canonical Polyadic (CP) Tensor factorization an
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Phan, Anh-Huy, Petr Tichavsky, and Andrzej Cichocki. "Rank-one tensor injection: A novel method for canonical polyadic tensor decomposition." In 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2016. http://dx.doi.org/10.1109/icassp.2016.7472137.

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Hou, Jingyao, Feng Zhang, Yao Wang, and Jianjun Wang. "Low-Tubal-Rank Tensor Recovery From One-Bit Measurements." In ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2020. http://dx.doi.org/10.1109/icassp40776.2020.9054163.

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Vandecappelle, Michiel, Nico Vervliet, and Lieven De Lathauwer. "Rank-one Tensor Approximation with Beta-divergence Cost Functions." In 2019 27th European Signal Processing Conference (EUSIPCO). IEEE, 2019. http://dx.doi.org/10.23919/eusipco.2019.8902937.

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Ghassemi, Mohsen, Zahra Shakeri, Anand D. Sarwate, and Waheed U. Bajwa. "STARK: Structured dictionary learning through rank-one tensor recovery." In 2017 IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP). IEEE, 2017. http://dx.doi.org/10.1109/camsap.2017.8313164.

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Hua, Gang, Paul A. Viola, and Steven M. Drucker. "Face Recognition using Discriminatively Trained Orthogonal Rank One Tensor Projections." In 2007 IEEE Conference on Computer Vision and Pattern Recognition. IEEE, 2007. http://dx.doi.org/10.1109/cvpr.2007.383107.

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Hongcheng Wang and N. Ahuja. "Compact representation of multidimensional data using tensor rank-one decomposition." In Proceedings of the 17th International Conference on Pattern Recognition, 2004. ICPR 2004. IEEE, 2004. http://dx.doi.org/10.1109/icpr.2004.1334001.

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Li, Ping, Jiashi Feng, Xiaojie Jin, Luming Zhang, Xianghua Xu, and Shuicheng Yan. "Online Robust Low-Rank Tensor Learning." In Twenty-Sixth International Joint Conference on Artificial Intelligence. International Joint Conferences on Artificial Intelligence Organization, 2017. http://dx.doi.org/10.24963/ijcai.2017/303.

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The rapid increase of multidimensional data (a.k.a. tensor) like videos brings new challenges for low-rank data modeling approaches such as dynamic data size, complex high-order relations, and multiplicity of low-rank structures. Resolving these challenges require a new tensor analysis method that can perform tensor data analysis online, which however is still absent. In this paper, we propose an Online Robust Low-rank Tensor Modeling (ORLTM) approach to address these challenges. ORLTM dynamically explores the high-order correlations across all tensor modes for low-rank structure modeling. To
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