Tensor Decompositions and Applications

By Tamara G. Kolda, Brett W. Bader. 2009

10,682 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Mathematics, Representation & Self-Supervised Learning, Numerical Methods & Scientific Computing, Signal Processing

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Citations in the corpus

Beyond CCA: Moment Matching for Multi-View Models (2016, neutral): “Then, by the multilinearity property for cumulants, one obtains where × i denotes the i -mode tensor-matrix product (see, e.g., Kolda & Bader, 2009).”
Rethinking LDA: Moment Matching for Discrete ICA (2015, background): “x n0m E(x m)) 1 A 3 5 = 1 N X m E h (x m E(x m)) 2 i = 1 N X m var(x m): 11For tensors, such decomposition is also known under the names CANDECOMP/PARAFAC or, simply, the CP decomposition (see, e.g., [34]). 15 Further, by the law of total variance: E kbE(x) E(x)k2 2 = 1 N X m [E(var(x mjy)) + var(”
A literature survey of low‐rank tensor approximation techniques (2013, neutral): “Like CP, the Tucker decomposition has a long history and we refer to the survey [168] for a more detailed account.”
From Frequency to Meaning: Vector Space Models of Semantics (2010, methodology): “The generalization of a matrix is a tensor (Kolda & Bader, 2009; Acar & Yener, 2009).”
MUTAN: Multimodal Tucker Fusion for Visual Question Answering (2017, background): “A comprehensive discussion on Tucker decomposition and tensor analysis may be found in [12].”
coMobile: real-time human mobility modeling at urban scale using multi-view learning (2015, methodology): “Based on the classic Tucker decomposition model [13], we decompose A into a core tensor I along with three matrices, U ∈ RN×d , S ∈ RM×d , and T ∈ RK×d .”
Rotate your Networks: Better Weight Consolidation and Less Catastrophic Forgetting (2018, neutral): “See [22] for more details.”
Multi-Relational Latent Semantic Analysis (2013, methodology): “This produces a tensor S where each slice is a linear combination of the slices of G with coefficients given by T (see (Kolda and Bader, 2009) for detail).”
A semantic matching energy function for learning with multi-relational data (2013, background): “with Wl, Wr ∈ Rp×d×d (weights), bl, br ∈ R (biases) and ×̄3 denotes the n-mode vector-tensor product along the 3 mode (see Kolda and Bader (2009) for more details).”
Natural Language Processing for EHR-Based Computational Phenotyping (2018, methodology): “[46], they applied tensor factorization [47], [48] on medication orders to generate phenotypes without supervision.”
Modeling Relational Data with Graph Convolutional Networks (2017, methodology): “Many of these approaches can be regarded as modifications or special cases of classic tensor decomposition methods such as CP or Tucker; for a comprehensive overview of tensor decomposition literature we refer the reader to Kolda and Bader [20].”
Compression of fully-connected layer in neural network by Kronecker product (2015, background): “×p is the tensor-matrix product over mode p [14], which can be implemented as a matrix product following a linear time unfolding operation of tensor.”
Speeding-up Convolutional Neural Networks Using Fine-tuned CP-Decomposition (2014, methodology): “Unfortunately, this is not the case for the CP-decomposition when d > 2 , as there is no ﬁnite algorithm for determining canonical rank of a tensor (Kolda & Bader, 2009).”
Compression of Deep Convolutional Neural Networks for Fast and Low Power Mobile Applications (2015, methodology): “For more information on the tensor decomposition, the reader is referred to the survey paper (Kolda & Bader, 2009).”
Distributional Memory: A General Framework for Corpus-Based Semantics (2010, positive): “More explicitly, in mode-n matricization we map each tensor entry ( i 1 , i 2 , ... , i N ) to matrix entry ( i n , j ), where j is computed as in Equation (1), adapted from Kolda and Bader (2009).”
A Review of Relational Machine Learning for Knowledge Graphs (2015, methodology): “Connection to Tensor Factorization: RESCAL is similar to methods used in recommendation systems [66], and to traditional tensor factorization methods [67].”
Meta-Curvature (2019, background): “We refer the reader to [17] for a more comprehensive review.”
Deep Multi-task Representation Learning: A Tensor Factorisation Approach (2016, methodology): “Tucker Decomposition Given an N -way tensor of size Tucker decomposition is usually implemented by an alternating least squares (ALS) method [Kolda and Bader, 2009].”
Inductive Bias of Deep Convolutional Networks through Pooling Geometry (2016, background): “4 is an instance of the classic CP decomposition, also known as rank-1 decomposition (see [16] for a historic survey).”
Tensor decompositions for learning latent variable models (2012, background): “ous science and engineering disciplines, including neuroscience, phylogenetics, signal processing, data mining, and computer vision. A thorough survey of these techniques and applications is given by Kolda and Bader (2009). Below, we discuss a few speciﬁc connections to two applications in machine l”