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Online Learning in Tensor Space
"... We propose an online learning algorithm based on tensorspace models. A tensorspace model represents data in a compact way, and via rank1 approximation the weight tensor can be made highly structured, resulting in a significantly smaller number of free parameters to be estimated than in comparabl ..."
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We propose an online learning algorithm based on tensorspace models. A tensorspace model represents data in a compact way, and via rank1 approximation the weight tensor can be made highly structured, resulting in a significantly smaller number of free parameters to be estimated than
Natural Projectors in Tensor Spaces∗
"... Abstract. The aim of this paper is to introduce a method of invariant decompositions of the tensor space T rsR n = Rn ⊗Rn ⊗ · · · ⊗Rn ⊗Rn ∗ ⊗Rn ∗ ⊗ · · · ⊗Rn∗ (r factors Rn, s factors the dual vector space Rn∗), endowed with the tensor representation of the general linear group GLn(R). The ..."
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Abstract. The aim of this paper is to introduce a method of invariant decompositions of the tensor space T rsR n = Rn ⊗Rn ⊗ · · · ⊗Rn ⊗Rn ∗ ⊗Rn ∗ ⊗ · · · ⊗Rn∗ (r factors Rn, s factors the dual vector space Rn∗), endowed with the tensor representation of the general linear group GLn
ON ENDOMORPHISMS OF QUANTUM TENSOR SPACE
, 806
"... Abstract. We give a presentation of the endomorphism algebra End Uq(sl2)(V ⊗r), where V is the 3dimensional irreducible module for quantum sl2 over the function field C(q 1 2). This will be as a quotient of the BirmanWenzlMurakami algebra BMWr(q): = BMWr(q −4, q2 −q −2) by an ideal generated by a ..."
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is the classical realisation of the TemperleyLieb algebra on tensor space. In particular, we show that all relations among the endomorphisms defined by the Rmatrices on V ⊗r are consequences of relations among the three Rmatrices acting on V ⊗4. The proof makes extensive use of the theory of cellular algebras
Novel View Synthesis in Tensor Space
 In Proc. of IEEE Conference on Computer Vision and Pattern Recognition
, 1997
"... We present a new method for synthesizing novel views of a 3D scene from few model images in full correspondence. The core of this work is the derivation of a tensorial operator that describes the transformation from a given tensor of three views to a novel tensor of a new configuration of three view ..."
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Cited by 115 (8 self)
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We present a new method for synthesizing novel views of a 3D scene from few model images in full correspondence. The core of this work is the derivation of a tensorial operator that describes the transformation from a given tensor of three views to a novel tensor of a new configuration of three
Orthogonal bases of symmetrized tensor spaces
 LINEAR AND MULTILINEAR ALGEBRA 39
, 1995
"... It is shown that a symmetrized tensor space does not have an orthogonal basis consisting of standard symmetrized tensors if the associated permutation group is 2transitive. In particular, no such basis exists if the group is the symmetric group or the alternating group as conjectured by T.Y. Tam ..."
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Cited by 10 (3 self)
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It is shown that a symmetrized tensor space does not have an orthogonal basis consisting of standard symmetrized tensors if the associated permutation group is 2transitive. In particular, no such basis exists if the group is the symmetric group or the alternating group as conjectured by T.Y. Tam
Tensor space model for document analysis
, 2006
"... Vector Space Model (VSM) has been at the core of information retrieval for the past decades. VSM considers the documents as vectors in high dimensional space. In such a vector space, techniques like Latent Semantic Indexing (LSI), Support Vector Machines (SVM), Naive Bayes, etc., can be then applied ..."
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Cited by 11 (1 self)
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be then applied for indexing and classification. However, in some cases, the dimensionality of the document space might be extremely large, which makes these techniques infeasible due to the curse of dimensionality. In this paper, we propose a novel Tensor Space Model for document analysis. We represent documents
Tensor Space Models for Authorship Identification
"... Abstract. Authorship identification can be viewed as a text categorization task. However, in this task the most frequent features appear to be the most important discriminators, there is usually a shortage of training texts, and the training texts are rarely evenly distributed over the authors. To c ..."
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. To cope with these problems, we propose tensors of second order for representing the stylistic properties of texts. Our approach requires the calculation of much fewer parameters in comparison to the traditional vector space representation. We examine various methods for building appropriate tensors
THE COEFFICIENT COALGEBRA OF A SYMMETRIZED TENSOR SPACE
"... Abstract. The coefficient coalgebra of rfold tensor space and its dual, the Schur algebra, are generalized in such a way that the role of the symmetric group Σr is played by an arbitrary subgroup of Σr. The dimension of the coefficient coalgebra of a symmetrized tensor space is computed and the dua ..."
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Abstract. The coefficient coalgebra of rfold tensor space and its dual, the Schur algebra, are generalized in such a way that the role of the symmetric group Σr is played by an arbitrary subgroup of Σr. The dimension of the coefficient coalgebra of a symmetrized tensor space is computed
Linear operators and positive semidefiniteness of symmetric tensor spaces
, 2013
"... Abstract We study symmetric tensor spaces and cones arising from polynomial optimization and physical sciences. We prove a decomposition invariance theorem for linear operators over the symmetric tensor space, which leads to several other interesting properties in symmetric tensor spaces. We then co ..."
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Abstract We study symmetric tensor spaces and cones arising from polynomial optimization and physical sciences. We prove a decomposition invariance theorem for linear operators over the symmetric tensor space, which leads to several other interesting properties in symmetric tensor spaces. We
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