Relevant bibliographies by topics / Subspaces

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Subspaces'

Author: Grafiati
Published: 4 June 2021
Last updated: 25 July 2025

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Journal articles on the topic "Subspaces"

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Baranov, Anton, and Harald Woracek. "Subspaces of de Branges Spaces Generated by Majorants." Canadian Journal of Mathematics 61, no. 3 (2009): 503–17. http://dx.doi.org/10.4153/cjm-2009-026-2.

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Abstract.For a given de Branges space ℋ (E ) we investigate de Branges subspaces defined in terms of majorants on the real axis. If ω is a nonnegative function on ℝ, we consider the subspaceWe show that ℛω (E ) is a de Branges subspace and describe all subspaces of this form. Moreover, we give a criterion for the existence of positive minimal majorants.
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Wang, Junpeng, Xiaotong Liu, and Han-Wei Shen. "High-dimensional data analysis with subspace comparison using matrix visualization." Information Visualization 18, no. 1 (2017): 94–109. http://dx.doi.org/10.1177/1473871617733996.

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Due to the intricate relationship between different dimensions of high-dimensional data, subspace analysis is often conducted to decompose dimensions and give prominence to certain subsets of dimensions, i.e. subspaces. Exploring and comparing subspaces are important to reveal the underlying features of subspaces, as well as to portray the characteristics of individual dimensions. To date, most of the existing high-dimensional data exploration and analysis approaches rely on dimensionality reduction algorithms (e.g. principal component analysis and multi-dimensional scaling) to project high-di
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Neckrasov, Vasiliy. "On Some Properties of Irrational Subspaces." Uniform distribution theory 17, no. 1 (2022): 89–104. http://dx.doi.org/10.2478/udt-2022-0002.

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Abstract In this paper, we discuss some properties of completely irrational subspaces. We prove that there exist completely irrational subspaces that are badly approximable and, moreover, sets of such subspaces are winning in different senses. We get some bounds for Diophantine exponents of vectors that lie in badly approximable subspaces that are completely irrational; in particular, for any vector ξ from two-dimensional badly approximable completely irrational subspace of ℝ d one has ω ⌢ ( ξ ) ≤ 5 - 1 2 \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}\over \omega } \left( \xi \
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Sia, Florence, and Rayner Alfred. "Tree-based mining contrast subspace." International Journal of Advances in Intelligent Informatics 5, no. 2 (2019): 169. http://dx.doi.org/10.26555/ijain.v5i2.359.

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All existing mining contrast subspace methods employ density-based likelihood contrast scoring function to measure the likelihood of a query object to a target class against other class in a subspace. However, the density tends to decrease when the dimensionality of subspaces increases causes its bounds to identify inaccurate contrast subspaces for the given query object. This paper proposes a novel contrast subspace mining method that employs tree-based likelihood contrast scoring function which is not affected by the dimensionality of subspaces. The tree-based scoring measure recursively bin
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Wang, Xuan, Chao Sun, Ming Yang Li, and Shao-Dong Zhang. "Detection by Angle-domain subspace with horizontal array in uncertain shallow-water environment." Acta Physica Sinica 71, no. 8 (2022): 1. http://dx.doi.org/10.7498/aps.71.20211742.

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The uncertainty of environmental parameters affects the robustness of detection method in complex shallow water. We define the angle-domain subspaces with horizontal linear array and estimate it in a proper way in the uncertain environment. Based on the angle-domain subspaces, we propose an angle-domain subspace detector and its robust form. Angle-domain subspaces contain the uncertain informations by using the observation matrices in different environmental parameters. The relationship between the horizontal wave number of propagating modes and the sound speed of the bottom and sediment in ha
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Shi, Yanyue, and Na Zhou. "Reducing Subspaces of Some Multiplication Operators on the Bergman Space over Polydisk." Abstract and Applied Analysis 2015 (2015): 1–12. http://dx.doi.org/10.1155/2015/209307.

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We consider the reducing subspaces ofMzNonAα2(Dk), wherek≥3,zN=z1N1⋯zkNk, andNi≠Njfori≠j. We prove that each reducing subspace ofMzNis a direct sum of some minimal reducing subspaces. We also characterize the minimal reducing subspaces in the cases thatα=0andα∈(-1,+∞)∖Q, respectively. Finally, we give a complete description of minimal reducing subspaces ofMzNonAα2(D3)withα>-1.
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LENG, JINSONG, and ZHIHU HUANG. "OUTLIERS DETECTION WITH CORRELATED SUBSPACES FOR HIGH DIMENSIONAL DATASETS." International Journal of Wavelets, Multiresolution and Information Processing 09, no. 02 (2011): 227–36. http://dx.doi.org/10.1142/s0219691311004067.

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Detecting outliers in high dimensional datasets is quite a difficult data mining task. Mining outliers in subspaces seems to be a promising solution, because outliers may be embedded in some interesting subspaces. Due to the existence of many irrelevant dimensions in high dimensional datasets, it is of great importance to eliminate the irrelevant or unimportant dimensions and identify outliers in interesting subspaces with strong correlation. Normally, the correlation among dimensions can be determined by traditional feature selection techniques and subspace-based clustering methods. The dimen
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Fatehi, Kavan, Mohsen Rezvani, Mansoor Fateh, and Mohammad-Reza Pajoohan. "Subspace Clustering for High-Dimensional Data Using Cluster Structure Similarity." International Journal of Intelligent Information Technologies 14, no. 3 (2018): 38–55. http://dx.doi.org/10.4018/ijiit.2018070103.

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This article describes how recently, because of the curse of dimensionality in high dimensional data, a significant amount of research has been conducted on subspace clustering aiming at discovering clusters embedded in any possible attributes combination. The main goal of subspace clustering algorithms is to find all clusters in all subspaces. Previous studies have mostly been generating redundant subspace clusters, leading to clustering accuracy loss and also increasing the running time of the algorithms. A bottom-up density-based approach is suggested in this article, in which the cluster s
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Wang, Xing, Jun Wang, Carlotta Domeniconi, Guoxian Yu, Guoqiang Xiao, and Maozu Guo. "Multiple Independent Subspace Clusterings." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 5353–60. http://dx.doi.org/10.1609/aaai.v33i01.33015353.

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Multiple clustering aims at discovering diverse ways of organizing data into clusters. Despite the progress made, it’s still a challenge for users to analyze and understand the distinctive structure of each output clustering. To ease this process, we consider diverse clusterings embedded in different subspaces, and analyze the embedding subspaces to shed light into the structure of each clustering. To this end, we provide a two-stage approach called MISC (Multiple Independent Subspace Clusterings). In the first stage, MISC uses independent subspace analysis to seek multiple and statistical ind
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Gopinath, S., G. Kowsalya, K. Sakthivel, and S. Arularasi. "A Proposed Clustering Algorithm for Efficient Clustering of High-Dimensional Data." Journal of Information Technology and Cryptography 1, no. 1 (2023): 14–21. http://dx.doi.org/10.48001/joitc.2023.1114-21.

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To partition transaction data values, clustering algorithms are used. To analyse the relationships between transactions, similarity measures are utilized. Similarity models based on vectors perform well with low-dimensional data. High-dimensional data values are clustered using subspace clustering techniques. Clustering high-dimensional data is difficult due to the curse of dimensionality. Projective clustering seeks out projected clusters in subsets of a data space's dimensions. In high-dimensional data space, a probability model represents predicted clusters. A model-based fuzzy projection c
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Dissertations / Theses on the topic "Subspaces"

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Chowdhury, Ameerah. "Colouring Subspaces." Thesis, University of Waterloo, 2005. http://hdl.handle.net/10012/1026.

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This thesis was originally motivated by considering vector space analogues of problems in extremal set theory, but our main results concern colouring a graph that is intimately related to these vector space analogues. The vertices of the <em>q</em>-Kneser graph are the <em>k</em>-dimensional subspaces of a vector space of dimension <em>v</em> over F<sub><em>q</em></sub>, and two <em>k</em>-subspaces are adjacent if they have trivial intersection. The new results in this thesis involve colouring the <em>q</em>-Kneser graph when <em>k</em>=2. There are two cases. When <em>k</em>=2 and <e
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Al, Sadoon Trujillo Majid. "Causality along subspaces." Thesis, University of Cambridge, 2011. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.609157.

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Ricks, Russell M. "Planar CAT(k) Subspaces." Diss., CLICK HERE for online access, 2010. http://contentdm.lib.byu.edu/ETD/image/etd3420.pdf.

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Savin, Anton, Bert-Wolfgang Schulze, and Boris Sternin. "Elliptic operators in subspaces." Universität Potsdam, 2000. http://opus.kobv.de/ubp/volltexte/2008/2570/.

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We construct elliptic theory in the subspaces, determined by pseudodifferential projections. The finiteness theorem as well as index formula are obtained for elliptic operators acting in the subspaces. Topological (K-theoretic) aspects of the theory are studied in detail.
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Adams, Lynn I. "Classifying Triply-Invariant Subspaces." University of Akron / OhioLINK, 2007. http://rave.ohiolink.edu/etdc/view?acc_num=akron1185565121.

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Savin, Anton, and Boris Sternin. "Elliptic operators in even subspaces." Universität Potsdam, 1999. http://opus.kobv.de/ubp/volltexte/2008/2546/.

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An elliptic theory is constructed for operators acting in subspaces defined via even pseudodifferential projections. Index formulas are obtained for operators on compact manifolds without boundary and for general boundary value problems. A connection with Gilkey's theory of η-invariants is established.
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Savin, Anton, and Boris Sternin. "Elliptic operators in odd subspaces." Universität Potsdam, 1999. http://opus.kobv.de/ubp/volltexte/2008/2547/.

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An elliptic theory is constructed for operators acting in subspaces defined via even pseudodifferential projections. Index formulas are obtained for operators on compact manifolds without boundary and for general boundary value problems. A connection with Gilkey's theory of η-invariants is established.
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Mahvidi, Ali. "Invariant subspaces of composition operators." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape9/PQDD_0020/NQ45739.pdf.

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POSTERNAK, REGINA. "INVARIANT SUBSPACES FOR HIPONORMAL OPERATORS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2002. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=3338@1.

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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO<br>O problema do subespaço invariante consiste na seguinte pergunta: será que todo operador (i.e., transformação linear limitada) atuando em um espaço de Hilbert separável (complexo de dimensão infinita) tem subespaço invariante nãotrivial? Este é, possivelmente, o mais importante problema em aberto na teoria de operadores. Em particular, o problema do subespaço invariante permanece em aberto (pelo menos até a presente data) para operadores hiponormais, ou seja, ainda não se sabe se todo operador hiponormal (atuando em um espaço de
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Ahuja, Kapil. "Recycling Krylov Subspaces and Preconditioners." Diss., Virginia Tech, 2011. http://hdl.handle.net/10919/29539.

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Science and engineering problems frequently require solving a sequence of single linear systems or a sequence of dual linear systems. We develop algorithms that recycle Krylov subspaces and preconditioners from one system (or pair of systems) in the sequence to the next, leading to efficient solutions. Besides the benefit of only having to store few Lanczos vectors, using BiConjugate Gradients (BiCG) to solve dual linear systems may have application-specific advantages. For example, using BiCG to solve the dual linear systems arising in interpolatory model reduction provides a backward err
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Books on the topic "Subspaces"

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Radjavi, Heydar. Invariant subspaces. 2nd ed. Dover Publications, 2003.

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Henry, Helson, Yadav B. S. 1931-, Singh Udita Narayana 1917-1989, University of Delhi. Dept. of Mathematics., and International Conference on "Invariant Subspaces and Allied Topics" (1986 : Dept. of Mathematics, University of Delhi), eds. Invariant subspaces and allied topics. Narosa Pub. House, 1990.

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Mashreghi, Javad, Emmanuel Fricain, and William Ross, eds. Invariant Subspaces of the Shift Operator. American Mathematical Society, 2015. http://dx.doi.org/10.1090/conm/638.

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1929-, Lancaster Peter, and Rodman L, eds. Invariant subspaces of matrices with applications. Wiley, 1986.

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MacDonald, Gordon Wilson. Invariant subspaces for weighted translation operators. [s.n.], 1989.

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Pestman, Wiebe Roelf. Group representations on Hilbert subspaces of distributions. [s.n.], 1985.

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Chalendar, Isabelle. Modern approaches to the invariant-subspace problem. Cambridge University Press, 2011.

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Demmel, James Weldon. Three methods for refining estimates of invariant subspaces. Courant Institute of Mathematical Sciences, New York University, 1985.

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Kadelburg, Zoran. Subspaces and quotients of topological and ordered vector spaces. University of Novi Sad, Institute of Mathematics, 1997.

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Bisztriczky, T. On hyperplanes and free subspaces of affine Klingenberg spaces. Dept. of Mathematics, University of Toronto, 1992.

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Book chapters on the topic "Subspaces"

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Smith, Larry. "Subspaces." In Linear Algebra. Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4612-1670-4_4.

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Kantor, I. L., and A. S. Solodovnikov. "Subspaces." In Hypercomplex Numbers. Springer New York, 1989. http://dx.doi.org/10.1007/978-1-4612-3650-4_10.

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Dolićanin, Ćemal B., and Anatolij B. Antonevich. "Subspaces." In Dynamical Systems Generated by Linear Maps. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-08228-8_6.

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Dybin, Vladimir, and Sergei M. Grudsky. "Model Subspaces." In Introduction to the Theory of Toeplitz Operators with Infinite Index. Birkhäuser Basel, 2002. http://dx.doi.org/10.1007/978-3-0348-8213-2_4.

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Hedenmalm, Haakan, Boris Korenblum, and Kehe Zhu. "Invariant Subspaces." In Graduate Texts in Mathematics. Springer New York, 2000. http://dx.doi.org/10.1007/978-1-4612-0497-8_6.

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Golan, Jonathan S. "Krylov Subspaces." In The Linear Algebra a Beginning Graduate Student Ought to Know. Springer Netherlands, 2012. http://dx.doi.org/10.1007/978-94-007-2636-9_13.

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Nikol’skiĭ, Nikolaĭ K. "Invariant Subspaces." In Grundlehren der mathematischen Wissenschaften. Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/978-3-642-70151-1_2.

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Hackbusch, Wolfgang. "Minimal Subspaces." In Tensor Spaces and Numerical Tensor Calculus. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-28027-6_6.

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Kubrusly, Carlos S. "Invariant Subspaces." In Hilbert Space Operators. Birkhäuser Boston, 2003. http://dx.doi.org/10.1007/978-1-4612-2064-0_1.

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Kubrusly, Carlos S. "Reducing Subspaces." In Hilbert Space Operators. Birkhäuser Boston, 2003. http://dx.doi.org/10.1007/978-1-4612-2064-0_4.

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Conference papers on the topic "Subspaces"

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Kalenov, N. E., G. I. Savin, and A. N. Sotnikov. "The Architecture of the Common Digital Space of Scientific Knowledge." In Всероссийская научная конференция "Единое цифровое пространство научных знаний: проблемы и решения". Москва, Берлин: Директмедиа Паблишинг, 2021. http://dx.doi.org/10.51218/978-5-4499-1905-2-2021-7-16.

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The architecture of the Common Digital Space of Scientific &#x0D; Knowledge (CDSSK) is determined by its functions and objectives. CDSSK includes a set of subspaces related to various scientific fields. The unity of subspaces is provided by unified principles for constructing subspaces and ontological connections between their objects. Each subspace includes digital objects, metadata containing facts related to objects, and subject onotologies that provide advanced searches and navigation through space. All &#x0D; information is reflected in the CDSSK according to the rules of the «semantic WE
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Renaud, J. E., and G. A. Gabriele. "Sequential Global Approximation in Non-Hierarchic System Decomposition and Optimization." In ASME 1991 Design Technical Conferences. American Society of Mechanical Engineers, 1991. http://dx.doi.org/10.1115/detc1991-0086.

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Abstract A procedure for the optimization of non-hierarchic systems by decomposition into reduced subspaces is presented. Sequential global approximation is proposed as a coordination procedure for subspace optimizations. The same objective function and cumulative constraints are imposed at each subspace. Non-local functions are approximated at the subspaces using global sensitivities. The method optimizes the subspace problems concurrently allowing for parallel processing. Following each sequence of concurrent subspace optimizations an approximation to the global problem is formed using desig
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Zhou, Lei, Xiao Bai, Dong Wang, Xianglong Liu, Jun Zhou, and Edwin Hancock. "Latent Distribution Preserving Deep Subspace Clustering." 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.2019/617.

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Subspace clustering is a useful technique for many computer vision applications in which the intrinsic dimension of high-dimensional data is smaller than the ambient dimension. Traditional subspace clustering methods often rely on the self-expressiveness property, which has proven effective for linear subspace clustering. However, they perform unsatisfactorily on real data with complex nonlinear subspaces. More recently, deep autoencoder based subspace clustering methods have achieved success owning to the more powerful representation extracted by the autoencoder network. Unfortunately, these
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Ying, Shihui, Lipeng Cai, Changzhou He, and Yaxin Peng. "Geometric Understanding for Unsupervised Subspace Learning." 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.2019/579.

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In this paper, we address the unsupervised subspace learning from a geometric viewpoint. First, we formulate the subspace learning as an inverse problem on Grassmannian manifold by considering all subspaces as points on it. Then, to make the model computable, we parameterize the Grassmannian manifold by using an orbit of rotation group action on all standard subspaces, which are spanned by the orthonormal basis. Further, to improve the robustness, we introduce a low-rank regularizer which makes the dimension of subspace as low as possible. Thus, the subspace learning problem is transferred to
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Zhang, Zhao, Jiahuan Ren, Zheng Zhang, and Guangcan Liu. "Deep Latent Low-Rank Fusion Network for Progressive Subspace Discovery." In Twenty-Ninth International Joint Conference on Artificial Intelligence and Seventeenth Pacific Rim International Conference on Artificial Intelligence {IJCAI-PRICAI-20}. International Joint Conferences on Artificial Intelligence Organization, 2020. http://dx.doi.org/10.24963/ijcai.2020/383.

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Low-rank representation is powerful for recover-ing and clustering the subspace structures, but it cannot obtain deep hierarchical information due to the single-layer mode. In this paper, we present a new and effective strategy to extend the sin-gle-layer latent low-rank models into multi-ple-layers, and propose a new and progressive Deep Latent Low-Rank Fusion Network (DLRF-Net) to uncover deep features and struc-tures embedded in input data. The basic idea of DLRF-Net is to refine features progressively from the previous layers by fusing the subspaces in each layer, which can potentially obt
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Baron, Luc, and Jorge Angeles. "The Measurement Subspaces of Parallel Manipulators Under Sensor Redundancy." In ASME 1994 Design Technical Conferences collocated with the ASME 1994 International Computers in Engineering Conference and Exhibition and the ASME 1994 8th Annual Database Symposium. American Society of Mechanical Engineers, 1994. http://dx.doi.org/10.1115/detc1994-0158.

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Abstract Using the concept of measurement subspaces of the leg-end-point position of general parallel manipulators, a linear kinematic model is derived. For a class of 6-dof leg-kinematic architectures of general geometry, the sets of sensed joints that lead to a measurement subspace are classified into 16 different types. For each of these types, a geometric interpretation and the equations for the computation of the measurement subspace from the readouts of a set of sensed joints, are provided. The design rules on the sensing of parallel manipulators in order to obtain the linear kinematic m
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Iliopoulos, A. P., and J. G. Michopoulos. "Loading Subspace Selection for Multidimensional Characterization Tests via Computational Experiments." In ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/detc2010-28741.

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To pursue characterization of composite materials, contemporary automated material testing machines are programmed to follow loading paths in multidimensional spaces. A computational methodology for selecting the best loading subspace among all those possible is formulated and presented in this paper. The criterion for subspace selection employed is based on the assessment of which among the possible subspaces generates the richest set of strain-states as compared to those of the union of all possible 4D loading spaces. A systematic program of simulation sequences of virtual experiments is pre
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Sadeghi, Mostafa, Mohsen Joneidi, and H. B. Golestani. "Learning low-dimensional subspaces via sequential subspace fitting." In 2013 21st Iranian Conference on Electrical Engineering (ICEE). IEEE, 2013. http://dx.doi.org/10.1109/iraniancee.2013.6599895.

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Lodhi, Muhammad Asad, and Waheed U. Bajwa. "Union of Subspaces Signal Detection In Subspace Interference." In 2018 IEEE Statistical Signal Processing Workshop (SSP). IEEE, 2018. http://dx.doi.org/10.1109/ssp.2018.8450694.

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Tripathy, Rohit, and Ilias Bilionis. "Deep Active Subspaces: A Scalable Method for High-Dimensional Uncertainty Propagation." In ASME 2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/detc2019-98099.

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Abstract A problem of considerable importance within the field of uncertainty quantification (UQ) is the development of efficient methods for the construction of accurate surrogate models. Such efforts are particularly important to applications constrained by high-dimensional uncertain parameter spaces. The difficulty of accurate surrogate modeling in such systems, is further compounded by data scarcity brought about by the large cost of forward model evaluations. Traditional response surface techniques, such as Gaussian process regression (or Kriging) and polynomial chaos are difficult to sca
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Reports on the topic "Subspaces"

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Van Veen, Barry. Signal Processing in Subspaces. Defense Technical Information Center, 1997. http://dx.doi.org/10.21236/ada324997.

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Van Veen, Barry D., and Chong H. Lee. Adaptive Detection in Subspaces. Defense Technical Information Center, 1990. http://dx.doi.org/10.21236/ada231023.

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Mathew, T. Hermitian and Nonnegativity Preserving Subspaces. Defense Technical Information Center, 1985. http://dx.doi.org/10.21236/ada160294.

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Dongarra, J. J., S. Hammarling, and J. H. Wilkinson. Numerical considerations in computing invariant subspaces. Office of Scientific and Technical Information (OSTI), 1990. http://dx.doi.org/10.2172/6427540.

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Duarte, Marco F., Chinmay Hegde, Volkan Cevher, and Richard G. Baraniuk. Recovery of Compressible Signals in Unions of Subspaces. Defense Technical Information Center, 2009. http://dx.doi.org/10.21236/ada520217.

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Berner, Chad. Shift-invariant subspaces of locally compact abelian groups. Iowa State University, 2021. http://dx.doi.org/10.31274/cc-20240624-1284.

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Williams, Brian J., Kayla Coleman, Ralph C. Smith, and Max D. Morris. Gradient-Free Construction of Active Subspaces for Dimension Reduction. Office of Scientific and Technical Information (OSTI), 2019. http://dx.doi.org/10.2172/1523205.

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Ron, Amos, and Zuowei Shen. Frames and Stable Bases for Shift-Invariant Subspaces of L2(IRd). Defense Technical Information Center, 1994. http://dx.doi.org/10.21236/ada276470.

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DE Boor, Carl, Ronald A. DeVore, and Amos Ron. Approximation from Shift-Invariant Subspaces of L sup 2 (R sup d). Defense Technical Information Center, 1991. http://dx.doi.org/10.21236/ada238165.

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Byrd, Richard H., Robert B. Schnabel, and Gerald A. Shultz. Approximate Solution of the Trust Region Problem by Minimization Over Two-Dimensional Subspaces,. Defense Technical Information Center, 1986. http://dx.doi.org/10.21236/ada176527.

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You might also be interested in the extended bibliographies on the topic 'Subspaces' for particular source types:
Journal articles Dissertations / Theses Books
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