Some mathematical notes on three-mode factor analysis

By L. Tucker. 1966

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Citations in the corpus

A semantic matching energy function for learning with multi-relational data (2013, background): “(CP) (Harshman and Lundy 1994) or those from (Tucker 1966) have been applied on multirelational graphs.”
Deeper, Broader and Artier Domain Generalization (2017, positive): “Motivated by the well-known Tucker decomposition [28], we assume that the M -order tensorW is synthesized as:”
Compression of Deep Convolutional Neural Networks for Fast and Low Power Mobile Applications (2015, methodology): “Under this variant called Tucker-2 decomposition (Tucker, 1966), the kernel tensor is decomposed to: where C is a core tensor of size D × D × R 3 × R 4 .”
Deep Multi-task Representation Learning: A Tensor Factorisation Approach (2016, methodology): “Unlike matrix factorisation, there are multiple deﬁnitions of tensor factorisation, and we use Tucker [Tucker, 1966] and Tensor Train (TT) [Oseledets, 2011] decompositions.”
TuckER: Tensor Factorization for Knowledge Graph Completion (2019, methodology): “In this paper, we introduce TuckER (E stands for entities, R for relations), a straightforward linear model for link prediction on knowledge graphs, based on Tucker decomposition (Tucker, 1966) of the binary tensor of triples, acting as a strong baseline for more elaborate models.”
Probabilistic Models for Incomplete Multi-dimensional Arrays (2009, methodology): “The well-known models include the Tucker family ( Tucker, 1966 ), the PARAFAC family (Carroll & Chang, 1970; Harshman, 1972) and Higher-Order Singular Value Decomposition (HOSVD) (Lathauwer et al., 2000).”
Wedderburn Rank Reduction and Krylov Subspace Method for Tensor Approximation. Part 1: Tucker Case (2010, background): “The (truncated) Tucker decomposition/approximation [35] of A reads”
Cross approximation in tensor electron density computations (2010, methodology): “The (truncated‡) Tucker decomposition [21] of a tensor F=[ fij.”
TT-cross approximation for multidimensional arrays (2010, methodology): “Instead of it, for construction of the black-box approximation it was proposed in [34] to use the Tucker decomposition of the form [38]”
Learning Attribute-to-Feature Mappings for Cold-Start Recommendations (2010, methodology): “Bear in mind that the general framework presented here can be applied to other matrix factorization models, as well as to any other model where the entities of the application domain are represented by latent feature vectors, like Tucker decomposition [27] or PARAFAC [11].”
Fusing Hyperspectral and Multispectral Images via Coupled Sparse Tensor Factorization (2018, methodology): “As one of the most effective tensor decomposition methods, Tucker decomposition [38] factors a tensor as a core tensor multiplied by the factor matrix along each mode.”
Compositional Matrix-Space Models of Language (2010, methodology): “Then tensor decomposition techniques can be applied in order to find a compact representation, reduce noise, and cluster together similar tokens (Tucker, 1966; Rendle et al., 2009).”
Deep Hyperspectral Image Sharpening (2018, unknown): “Based on the Tucker decomposition [44], the HR-HSI is approximated by the core tensor”
On tensor approximation of Green iterations for Kohn-Sham equations (2008, methodology): “They were generally treated as methods for statistical data processing [32,35] with moderate accuracy requirements.”
Tensor decomposition of EEG signals: a brief review. (2015, unknown): “For a given N th-order tensor X ∈ decomposition is expressed as follows where rank-one tensor To avoid unnecessary confusion, we denote the component in the Tucker decomposition by a instead of u in the CPD Therefore, the Tucker decomposition is the sum of the rank-one tensors plus the error tensor.”