Multi-Way Analysis: Applications in the Chemical Sciences

By David E. Booth. 2005

668 citations recorded by the source corpus.

Subfields: Analytical Chemistry, Computer Vision and Pattern Recognition, Management Science and Operations Research

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Analytical Chemistry

In Computer Vision and Pattern Recognition

In Management Science and Operations Research

Citations in the corpus

A literature survey of low‐rank tensor approximation techniques (2013, neutral): “In this survey, we will focus on tensors that are induced by the discretization of a multivariate function; we refer to the survey [168] and to the books [174, 239] for the treatment of tensors containing observed data.”
missMDA: A Package for Handling Missing Values in Multivariate Data Analysis (2016, methodology): “However, we note that related algorithms have been suggested for other multi-table and multi-way methods, including PARAFAC (Tomasi and Bron 2005; Kroonenberg 2008; Acar, Dunlavy, Kolda, and Mrup 2011; Smilde, Bro, and Geladi 2004).”
All-at-once Optimization for Coupled Matrix and Tensor Factorizations (2011, background): “Tensor factorizations [3, 19, 29] can also be considered as one way of analyzing multiple matrices.”
CANDECOMP/PARAFAC Decomposition of High-Order Tensors Through Tensor Reshaping (2012, background): “…as Canonical polyadic decomposition (CPD), is a common tensor factorization which has found applications such as in chemometrics [3]–[5], telecommunication [6], [7], analysis of fMRI data [8], time-varying EEG spectrum [9], [10], data mining [11], A. H. Phan and A. Cichocki are with the Lab for…”
Algorithms for Numerical Analysis in High Dimensions (2005, background): “(cid:4) (cid:4) (cid:4) (cid:4) Since by deﬁnition ( s F ˜ l ) 2 = j c 2 j k (˜ l ), we have , and so we are still solving a linear least-squares problem.”
Third-Order Tensors as Operators on Matrices: A Theoretical and Computational Framework with Applications in Imaging (2013, background): “Third-order (and higher) tensors arise in a wide variety of application areas, including, but not limited to, chemometrics [24], psychometrics [13], and image and signal processing [5, 15, 23, 17, 8, 20, 29, 28, 30].”
SUSTain: Scalable Unsupervised Scoring for Tensors and its Application to Phenotyping (2018, methodology): “In our experiments, the first term, thus the computation of MTTKRP, dominates the total cost.”
DFacTo: Distributed Factorization of Tensors (2014, background): “Tensor data appears naturally in a number of applications [1, 2].”
Hadamard, Khatri-Rao, Kronecker and Other Matrix Products (2008, neutral): “For a, b, c, d of size 3× 1 and scalars α and β, we have Tαa+βb = αTa + βTb, (54) Tab = −Tba, (55) Ta = −Ta, (56) Taa = 0, (57) TaTb = ba′ − a′bI3, (58) (TaTb)′ = TbTa, (59) TaTbTc = Tacb′ − b′cTa, (60) TaTbTa = −a′bTa, (61) TaTaTa = −a′aTa, (62) c′Tab = a′Tbc = b′Tca = −c′Tba = −b′Tac = −a′Tcb, (63”
Tensor decomposition of EEG signals: a brief review. (2015, positive): “Then, in addition to the two modes of time and space, the additional mode segment (also called as epoch or trial) is naturally born for the ERP data Furthermore, if the EEG data of one segment is transformed into the time-frequency domain, another mode called as frequency is yielded .”
Limestone: High-throughput candidate phenotype generation via tensor factorization (2014, background): “An overview of tensors can be found in [48–50].”
Factorization strategies for third-order tensors (2011, background): “Applications involving operations with tensors include chemometrics [41], psychometrics [24], signal processing [9] [27] [39], computer vision [44] [46] [45], data mining [1] [38], graph analysis [21], neuroscience [3] [30] [31], and many more.”
Efficient MATLAB Computations with Sparse and Factored Tensors (2007, neutral): “, [44] for properties of these operators.”
Most Tensor Problems Are NP-Hard (2009, background): “Most Tensor Problems Are NP-Hard CHRISTOPHER J. HILLAR, Mathematical Sciences Research Institute LEK-HENG LIM, University of Chicago We prove that multilinear (tensor) analogues of many ef.ciently computable problems in numerical linear algebra are NP-hard.”
On Fast Computation of Gradients for CANDECOMP/PARAFAC Algorithms (2012, methodology): “CP algorithms available in the literature compute all G ( n ) n = 1 , 2 , . . . , N either sequentially (in alternating algorithms [2, 8, 16, 18, 23,30,31]) or simultaneously (as in all-at-once algorithms [1,24–26,32,33], line-search [27, 33]).”
Rubik: Knowledge Guided Tensor Factorization and Completion for Health Data Analytics (2015, methodology): “For two matrices M , N , we have the following property of the Khatri-Rao product [30]: Update the bias tensor.”
Tensor Algebra and Multidimensional Harmonic Retrieval in Signal Processing for MIMO Radar (2010, background): “In practice, however, it is often desirable to impose application—specific constraints on the loadings of the PARAFAC decomposition.”
Hierarchical ALS Algorithms for Nonnegative Matrix and 3D Tensor Factorization (2007, methodology): “Nonnegative Matrix Factorization (NMF) and its multi-way extensions: Nonnegative Tensor Factorization (NTF) and Parallel Factor analysis (PARAFAC) models with sparsity and/or non-negativity constraints have been recently proposed as promising and quite efficient tools for processing sparse signals, ”