A new efficient method for determining the number of components in PARAFAC models
Rasmus Bro,Henk A.L. Kiers +1 more
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The core consistency diagnostic (CORCONDIA) as discussed by the authors is a diagnostic for determining the appropriate number of components for multiway models, which is based on scrutinizing the appropriateness of the structural model based on the data and the estimated parameters.Abstract:
A new diagnostic called the core consistency diagnostic (CORCONDIA) is suggested for determining the proper number of components for multiway models. It applies especially to the parallel factor analysis (PARAFAC) model, but also to other models that can be considered as restricted Tucker3 models. It is based on scrutinizing the ‘appropriateness’ of the structural model based on the data and the estimated parameters of gradually augmented models. A PARAFAC model (employing dimension-wise combinations of components for all modes) is called appropriate if adding other combinations of the same components does not improve the fit considerably. It is proposed to choose the largest model that is still sufficiently appropriate. Using examples from a range of different types of data, it is shown that the core consistency diagnostic is an effective tool for determining the appropriate number of components in e.g. PARAFAC models. However, it is also shown, using simulated data, that the theoretical understanding of CORCONDIA is not yet complete. Copyright © 2003 John Wiley & Sons, Ltd.read more
Citations
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Tensor Decompositions and Applications
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Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multi-way Data Analysis and Blind Source Separation
TL;DR: This book provides a broad survey of models and efficient algorithms for Nonnegative Matrix Factorization (NMF), including NMFs various extensions and modifications, especially Nonnegative Tensor Factorizations (NTF) and Nonnegative Tucker Decompositions (NTD).
Journal ArticleDOI
Fluorescence spectroscopy and multi-way techniques. PARAFAC
TL;DR: In this paper, a toolbox for MATLAB is presented to support improved visualisation and sensitivity analyses of PARAFAC models in fluorescence spectroscopy, demonstrated using a dissolved organic matter (DOM) fluorescence dataset.
Journal ArticleDOI
Distinguishing between terrestrial and autochthonous organic matter sources in marine environments using fluorescence spectroscopy
TL;DR: In this paper, the authors used parallel factor analysis (PARAFAC) of fluorescence spectra collected on trans-oceanic cruises in the Pacific and Atlantic oceans to investigate the optical characteristics of dissolved organic matter in waters with limited freshwater influence (salinity > 30).
Journal ArticleDOI
Organic Matter Fluorescence in Municipal Water Recycling Schemes: Toward a Unified PARAFAC Model
Kathleen R. Murphy,Adam Hambly,Sachin Singh,Rita K. Henderson,Andy Baker,Richard M. Stuetz,Stuart J. Khan +6 more
TL;DR: While the multimodel comparisons provide a compelling demonstration of PARAFAC's ability to distill chemical information from EEMs, deficiencies identified through this process have broad implications for interpreting and reusing (D)OM-PARAFAC models.
References
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Journal ArticleDOI
PARAFAC. Tutorial and applications
TL;DR: The multi-way decomposition method 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.
Journal ArticleDOI
The N-way Toolbox for MATLAB
Claus A. Andersson,Rasmus Bro +1 more
TL;DR: This communication is by no means an attempt to summarize or review the extensive work done in multiway data analysis but is intended solely for informing the reader of the existence, functionality, and applicability of the N-way Toolbox for MATLAB.
Book
Instrumental methods of chemical analysis
TL;DR: In this article, the authors present a course to make the student understand the advanced instrumentation available for chemical analysis, and the student would be able to choose the instrument needed for analysis.
Journal ArticleDOI
PARAFAC2 - Part II. Modeling chromatographic data with retention time shifts
TL;DR: In this paper, an approach for handling retention time shifts in resolving chromatographic data using the PARAFAC2 model is presented, where the matrix of elution profiles preserve its inner product structure from sample to sample.
Journal ArticleDOI
Exploratory study of sugar production using fluorescence spectroscopy and multi-way analysis
TL;DR: In this article, the authors used the unique parallel factor analysis (PARAFAC) model to decompose complex mixture signals into contributions from individual chemical components to analyze, understand, predict and monitor the quality based on a chemical foundation.
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