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TENSOR FUNCTIONS OF TENSORS AND THE CONCEPT OF EXTENDED TENSOR FIELDS.
, 2005
"... Abstract. Tensor fields depending on other tensor fields are considered. The concept of extended tensor fields is introduced and the theory of differentiation for such fields is developed. 1. Tensors and tensor fields on manifolds. Let M be some ndimensional smooth real manifold. Then each point p ..."
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Cited by 3 (1 self)
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Abstract. Tensor fields depending on other tensor fields are considered. The concept of extended tensor fields is introduced and the theory of differentiation for such fields is developed. 1. Tensors and tensor fields on manifolds. Let M be some ndimensional smooth real manifold. Then each point p
Eigenvalues, invariant factors, highest weights, and Schubert calculus
 Bull. Amer. Math. Soc. (N.S
"... Abstract. We describe recent work of Klyachko, Totaro, Knutson, and Tao, that characterizes eigenvalues of sums of Hermitian matrices, and decomposition of tensor products of representations of GLn(C). We explain related applications to invariant factors of products of matrices, intersections in Gra ..."
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Cited by 177 (3 self)
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Abstract. We describe recent work of Klyachko, Totaro, Knutson, and Tao, that characterizes eigenvalues of sums of Hermitian matrices, and decomposition of tensor products of representations of GLn(C). We explain related applications to invariant factors of products of matrices, intersections
Probabilistic Tensor Factorization for Tensor Completion
"... Multiway tensor datasets emerge naturally in a variety of domains, such as recommendation systems, bioinformatics, and retail data analysis. The data in these domains usually contains a large number of missing entries. Therefore, many applications in those domains aim at missing value prediction, w ..."
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Multiway tensor datasets emerge naturally in a variety of domains, such as recommendation systems, bioinformatics, and retail data analysis. The data in these domains usually contains a large number of missing entries. Therefore, many applications in those domains aim at missing value prediction
Characterizing RealValued Multivariate Complex Polynomials and Their Symmetric Tensor Representations
, 2014
"... In this paper we study multivariate polynomial functions in complex variables and the corresponding associated symmetric tensor representations. The focus is on finding conditions under which such complex polynomials/tensors always take real values. We introduce the notion of symmetric conjugate fo ..."
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Cited by 1 (1 self)
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In this paper we study multivariate polynomial functions in complex variables and the corresponding associated symmetric tensor representations. The focus is on finding conditions under which such complex polynomials/tensors always take real values. We introduce the notion of symmetric conjugate
Properties of Tensor Complementarity Problem and Some Classes of Structured Tensors
, 2014
"... This paper deals with the class of Qtensors, that is, a Qtensor is a real tensor A such that the tensor complementarity problem (q;A): nding x ∈ Rn such that x ≥ 0;q+Axm−1 ≥ 0; and x⊤(q+Axm−1) = 0; has a solution for each vector q ∈ Rn. Several subclasses of Qtensors are given: Ptensors, Rtens ..."
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Cited by 1 (0 self)
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This paper deals with the class of Qtensors, that is, a Qtensor is a real tensor A such that the tensor complementarity problem (q;A): nding x ∈ Rn such that x ≥ 0;q+Axm−1 ≥ 0; and x⊤(q+Axm−1) = 0; has a solution for each vector q ∈ Rn. Several subclasses of Qtensors are given: Ptensors, Rtensors
Pairwise Interaction Tensor Factorization for Personalized Tag Recommendation
"... Tagging plays an important role in many recent websites. Recommender systems can help to suggest a user the tags he might want to use for tagging a specific item. Factorization models based on the Tucker Decomposition (TD) model have been shown to provide high quality tag recommendations outperformi ..."
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Cited by 72 (11 self)
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outperforming other approaches like PageRank, FolkRank, collaborative filtering, etc. The problem with TD models is the cubic core tensor resulting in a cubic runtime in the factorization dimension for prediction and learning. In this paper, we present the factorization model PITF (Pairwise Interaction Tensor
1Uniqueness of Nonnegative Tensor Approximations
"... We show that a best nonnegative rankr approximation of a nonnegative tensor is almost always unique and that nonnegative tensors with nonunique best nonnegative rankr approximation form a semialgebraic set contained in an algebraic hypersurface. We then establish a singular vector variant of the P ..."
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of the Perron–Frobenius Theorem for positive tensors and apply it to show that a best nonnegative rankr approximation of a positive tensor can almost never be obtained by deflation. We show the subset of real tensors which admit more than one best rank one approximations is a hypersurface, and give a
Automatic reconstruction of Bspline surfaces of arbitrary topological type
 SIGGRAPH'96
, 1996
"... Creating freeform surfaces is a challenging task even with advanced geometric modeling systems. Laser range scanners offer a promising alternative for model acquisition—the 3D scanning of existing objects or clay maquettes. The problem of converting the dense point sets produced by laser scanners in ..."
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Cited by 173 (0 self)
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into useful geometric models is referred to as surface reconstruction. In this paper, we present a procedure for reconstructing a tensor product Bspline surface from a set of scanned 3D points. Unlike previous work which considers primarily the problem of fitting a single Bspline patch, our goal
Temporal Collaborative Filtering with Bayesian Probabilistic Tensor Factorization
"... Realworld relational data are seldom stationary, yet traditional collaborative filtering algorithms generally rely on this assumption. Motivated by our sales prediction problem, we propose a factorbased algorithm that is able to take time into account. By introducing additional factors for time, w ..."
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Cited by 61 (2 self)
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of analyzing largescale data sets. This new algorithm, called Bayesian Probabilistic Tensor Factorization (BPTF), is evaluated on several realworld problems including sales prediction and movie recommendation. Empirical results demonstrate the superiority of our temporal model. 1
A tensorbased algorithm for highorder graph matching
 In CVPR
, 2009
"... Abstract—This paper addresses the problem of establishing correspondences between two sets of visual features using higherorder constraints instead of the unary or pairwise ones used in classical methods. Concretely, the corresponding hypergraph matching problem is formulated as the maximization of ..."
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Cited by 84 (3 self)
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of a multilinear objective function over all permutations of the features. This function is defined by a tensor representing the affinity between feature tuples. It is maximized using a generalization of spectral techniques where a relaxed problem is first solved by a multidimensional power method
Results 11  20
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