Results 141 to 150 of about 1,580 (173)

Remedies for Degeneracy in Candecomp/Parafac

2016
In many psychological studies variables are measured for some subjects in different conditions. In these cases the available information is stored in a three-way data array. Three-way extensions of Principal Component Analysis have been introduced to summarize such an array through components.
GIORDANI, Paolo, ROCCI, Roberto
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A robust Parafac model for compositional data

Journal of Applied Statistics, 2017
ABSTRACTCompositional data are characterized by values containing relative information, and thus the ratios between the data values are of interest for the analysis. Due to specific features of compositional data, standard statistical methods should be applied to compositions expressed in a proper coordinate system with respect to an orthonormal basis.
M. A. Di Palma, P. Filzmoser, M. Gallo, K. Hron   +3 more
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Stability of CANDECOMP-PARAFAC tensor decomposition

2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2011
In this paper, stability of the CANDECOMP-PARAFAC (CP) tensor decomposition is addressed. It is done by deriving the Cramer-Rao lower bound (CRLB) on variance of an unbiased estimate of the tensor parameters, i.e. elements of its factor matrices, from its noisy observation (the tensor plus a random Gaussian i.i.d. tensor).
Petr Tichavský, Zbynek Koldovský
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Fundamentals of PARAFAC

2015
Abstract Parallel Factor Analysis (PARAFAC) is a popular multiway decomposition method for analytical data. This chapter introduces the PARAFAC model and the concepts of bilinearity and trilinearity of second-order data. The ALS algorithm to calculate the model, and the use of PARAFAC for calibration are also described. Practical aspects such as data
Ricard Boqué Martí, Joan Ferré Baldrich   +1 more
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PARAFAC. Tutorial and applications

Chemometrics and Intelligent Laboratory Systems, 1997
Abstract This paper explains the multi-way decomposition method PARAFAC and its use in chemometrics. PARAFAC is a generalization of PCA to higher order arrays, but some of the characteristics of the method are quite different from the ordinary two-way case.
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PARAFAC: Parallel factor analysis

Computational Statistics & Data Analysis, 1994
We review the method of Parallel Factor Analysis, which simultaneously fits multiple two-way arrays or ‘slices’ of a three-way array in terms of a common set of factors with differing relative weights in each ‘slice’. Mathematically, it is a straightforward generalization of the bilinear model of factor (or component) analysis (xij = ΣRr = 1airbjr) to ...
Harshman, R. A., Lundy, M. E.
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Candecomp/Parafac with ridge regularization

Chemometrics and Intelligent Laboratory Systems, 2013
Abstract The Candecomp/Parafac (CP) model decomposes a three-way array through components. In the practical use of CP, degeneracy may arise, i.e. CP parameter matrices with diverging, highly collinear and uninterpretable components. A frequently applied remedy to degeneracy is to fit a CP model with orthogonality constraints on one of the component ...
GIORDANI, Paolo, Roberto Rocci, ROCCI, Roberto   +2 more
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PARAFAC with splines: a case study

Journal of Chemometrics, 2002
AbstractThe PARAFAC model has been used in several applications in chemistry, e.g. for overlapped spectra resolution and second‐order calibration. In general, the PARAFAC method uses a vector space approach by considering the matrices resulting from the decomposition as a collection of vectors.
Marlon M. Reis, Márcia M. C. Ferreira
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Two-factor degeneracies and a stabilization of PARAFAC

Chemometrics and Intelligent Laboratory Systems, 1997
Abstract Mitchell and Burdick (B.C. Mitchell, D.S. Burdick, An empirical comparison of resolution methods for three-way arrays, Chemom. Intell. Lab. Syst. 20 (1993) 149–161; B.C. Mitchell, D.S. Burdick, Slowly converging PARAFAC sequences: Swamps and two-factor degeneracies, J. Chemom. 8 (1994) 155–168.) uncovered an intriguing correspondence between
William S Rayens
exaly   +2 more sources

Deflation method for CANDECOMP/PARAFAC tensor decomposition

2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2014
CANDECOMP/PARAFAC tensor decomposition (CPD) approximates multiway data by rank-1 tensors. Unlike matrix decomposition, the procedure which estimates the best rank-R tensor approximation through R sequential best rank-1 approximations does not work for tensors, because the deflation does not always reduce the tensor rank.
Anh Huy Phan 0001, Petr Tichavský, Andrzej Cichocki   +2 more
openaire   +1 more source