PARAFAC: parallel factor analysis

By Richard A. Harshman, M. E. Lundy. 1994

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Citations in the corpus

Irreflexive and Hierarchical Relations as Translations (2013, methodology): “In terms of scalability, models based on tensor factorization (like those from (Harshman & Lundy, 1994) or (Nickel et al., 2011)) have shown to be eﬃcient.”
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.”
Compression of Deep Convolutional Neural Networks for Fast and Low Power Mobile Applications (2015, methodology): “Two of the most popular tensor decomposition models are CANDECOMP/PARAFAC model (Carroll & Chang, 1970; Harshman & Lundy, 1994; Shashua & Hazan, 2005) and Tucker model (Tucker, 1966; De Lathauwer et al., 2000; Kim & Choi, 2007).”
Modeling multi‐way data with linearly dependent loadings (2009, methodology): “resolution and more generally for factor or component modeling of (multi-way) data such as constrained Tucker3 [1], PARAFAC [2,3], INDSCAL/CANDECOMP [4], window factor analysis [5], and multivariate curve resolution [6].”
Nonlinearities and Contextual Influences in Auditory Cortical Responses Modeled with Multilinear Spectrotemporal Methods (2008, unknown): “Other multilinear methods have been useful in various settings in the statistics and machine learning setting (e.g. Vasilescu and Terzopoulos, 2005; Tenenbaum and Freeman, 2000; Harshman and Lundy, 1994).”
Explainable Product Search with a Dynamic Relation Embedding Model (2019, methodology): “For instance, Harshman and Lundy [21] introduce a tensor factorization method for relation prediction.”
A Three-Way Model for Collective Learning on Multi-Relational Data (2011, methodology): “However, well-known tensor factorization approaches such as CANDECOMP/PARAFAC (CP) (Harshman & Lundy, 1994) or Tucker (Tucker, 1966) cannot model this collective learning effect sufficiently.”
Canonical polyadic decomposition of third-order tensors: relaxed uniqueness conditions and algebraic algorithm (2015, methodology): “ literature shows some variation in terminology. The CPD was introduced by F.L. Hitchcock in [16] and was later referred to as Canonical Decomposition (CANDECOMP) [2], Parallel Factor Model (PARAFAC) [12, 15], and Topographic Components Model [21]. Uniqueness of one factor matrix is called uni-mode ”
Tensor decompositions, alternating least squares and other tales (2009, methodology): “It has been later independently referred to as the Canonical Decomposition (CANDECOMP) [31] or Parallel Factor (PARAFAC) [32,33].”
Translating Embeddings for Modeling Multi-relational Data (2013, methodology): “…domain such as non-parametric Bayesian extensions of the stochastic blockmodel [7, 10, 17] and models based on tensor factorization [5] or collective matrix factorization [13, 11, 12], many of the most recent approaches have focused on increasing the expressivity and the…”
Shifted factor analysis—Part I: Models and properties (2003, background): “The acronyms stand for parallel factor analysis [21,42,45] and canonical decomposition [46] respectively.”
Harnessing the complexity of metabolomic data with chemometrics (2014, methodology): “They are usually designed to generalise singular value decomposition, and most of the existing approaches are unsupervised, including PARAFAC [69] and Tucker algorithms [70], but supervised alternatives also exist, for example, N-PLS [71].”
Channel Estimation for RIS-Empowered Multi-User MISO Wireless Communications (2020, methodology): “Recently, the PARAllel FACtor (PARAFAC) decomposition [36]–[40] has been considered as an efﬁcient method for estimating multiple large channel matrices in MIMO communication systems [41], [42].”
Tensorial extensions of independent component analysis for multisubject FMRI analysis (2005, methodology): “One such possible generalization is known as parallel factor analysis (PARAFAC3; Harshman (1970); Harshman and Lundy (1994)), where a three-way array is represented by a trilinear combination of three outer products: X ¼ XR r ar br cr þ E: Techniques like PARAFAC have gained popularity in some…”