Improving the speed of multi-way algorithms:

Andersson, Claus A.; Bro, Rasmus

doi:10.1016/s0169-7439(98)00010-0

Cited by 127 publications

(83 citation statements)

References 15 publications

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“…The algorithm took its name from the psychometrician Ledyard R. Tucker who proposed it in 1966 [22]. Several improvements were performed since then [8,23,24]. In this article, the authors decided to arrange the data in four dimensional arrays.…”

Section: Multidimensional Modeling: Tucker3mentioning

confidence: 99%

Bidimensional and Multidimensional Principal Component Analysis in Long Term Atmospheric Monitoring

et al. 2016

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Atmospheric monitoring produces huge amounts of data. Univariate and bivariate statistics are widely used to investigate variations in the parameters. To summarize information graphs are usually used in the form of histograms or tendency profiles (e.g., variable concentration vs. time), as well as bidimensional plots where two-variable correlations are considered. However, when dealing with big data sets at least two problems arise: a great quantity of numbers (statistics) and graphs are produced, and only two-variable interactions are often considered. The aim of this article is to show how the use of multivariate statistics helps in handling atmospheric data sets. Multivariate modeling considers all the variables simultaneously and returns the main results as bidimensional graphs that are easy-to-read. Principal Component Analysis (PCA; the most known multivariate method) and multiway-PCA (Tucker3) are compared from methodological and interpretative points of view. The article demonstrates the ability to emphasize different information depending on the data handling performed. The results and benefits achieved using a more complex model that allows for the simultaneous consideration of the entire variability of the system are compared with the results provided by the simpler but better-known model. Atmospheric monitoring (SO 2 , NO x , NO 2 , NO, and O 3 ) data from the Lake Como Area (Italy) since 1992 to 2007 were chosen for consideration for the case study.

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Section: Multidimensional Modeling: Tucker3mentioning

confidence: 99%

Bidimensional and Multidimensional Principal Component Analysis in Long Term Atmospheric Monitoring

et al. 2016

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“…In order to cope with the problem, we can use some modifications such as Compression [17] and Line Search [18,19]. The compression technique compresses the data into a smaller dimension core tensor using the TUCKER model.…”

Section: Communication Costmentioning

confidence: 99%

PARAFAC algorithms for large-scale problems

Phan

Cichocki

2011

Neurocomputing

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“…Kroonenberg showed that the algorithm converged if A, B, and C are orthonormal (Kroonenberg 1983). Andersson and Bro (1998) showed that for the estimation of the eigenvector matrices within the TuckALS3-algorithm, the Nonlinear Iterative Partial Least Squares (NIPALS)-algorithm is one of the most efficient approaches.…”

Section: Estimation Of the Tucker3 Modelmentioning

confidence: 99%