Robust PARAFAC for incomplete data

Hubert, Mia; Kerckhoven, Johan Van; Verdonck, Tim

doi:10.1002/cem.2452

Cited by 34 publications

(16 citation statements)

References 20 publications

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“…The PARAFAC model in terms of single elements of the data cube X ¼ ðx ijk Þ (i.e. for ith observation of jth variable in kth time), can be written as (Bro 1998;Harshman and Lundy 1994;Smilde et al 2004;Bosco et al 2006;Hubert et al 2012): Fig. 1 Three-way data structure-a graphical representation of the data array (cube) X and its slices X k , b the principle of unfolding the data cube X into data matrix X and the principle of centering and scaling of the unfolded data matrix X, c graphical representation of the formula (2) here e ijk stand for residuals.…”

Section: Three-way Analysis: Parafacmentioning

confidence: 99%

Normalization techniques for PARAFAC modeling of urine metabolomic data

et al. 2016

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Introduction One of the body fluids often used in metabolomics studies is urine. The concentrations of metabolites in urine are affected by hydration status of an individual, resulting in dilution differences. This requires therefore normalization of the data to correct for such differences. Two normalization techniques are commonly applied to urine samples prior to their further statistical analysis. First, AUC normalization aims to normalize a group of signals with peaks by standardizing the area under the curve (AUC) within a sample to the median, mean or any other proper representation of the amount of dilution. The second approach uses specific end-product metabolites such as creatinine and all intensities within a sample are expressed relative to the creatinine intensity. Objectives Another way of looking at urine metabolomics data is by realizing that the ratios between peak intensities are the information-carrying features. This opens up possibilities to use another class of data analysis techniques designed to deal with such ratios: compositional data analysis. The aim of this paper is to develop PARAFAC modeling of three-way urine metabolomics data in the context of compositional data analysis and compare this with standard normalization techniques. Methods In the compositional data analysis approach, special coordinate systems are defined to deal with the ratio problem. In essence, it comes down to using other distance measures than the Euclidian Distance that is used in the conventional analysis of metabolomic data. Results We illustrate using this type of approach in combination with three-way methods (i.e. PARAFAC) of a longitudinal urine metabolomics study and two simulations. In both cases, the advantage of the compositional approach is established in terms of improved interpretability of the scores and loadings of the PARAFAC model. Conclusion For urine metabolomics studies, we advocate the use of compositional data analysis approaches. They are easy to use, well established and proof to give reliable results.

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Section: Three-way Analysis: Parafacmentioning

confidence: 99%

Normalization techniques for PARAFAC modeling of urine metabolomic data

et al. 2016

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“…For example, in [11], alternating iteratively reweighted least squares (IRLS) using Huber influence functions was considered. In [12] alternating least absolute deviation (LAD) regression was proposed, while in [13] a robust PCA method was adapted to CP estimation. Alternating LAD regression was revisited in [14] and [15].…”

Section: Introductionmentioning

confidence: 99%

Canonical polyadic tensor decomposition in the presence of non Gaussian noise

Farias

Comon

2015

2015 23rd European Signal Processing Conference (EUSIPCO)

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In this paper we describe an estimator for the canonical polyadic (CP) tensor model using order statistics of the residuals. The estimator minimizes in an iterative and alternating fashion a dispersion function given by the weighted ranked absolute residuals. Specific choices of the weights lead to either equivalent or approximate versions of the least squares estimator, least absolute deviation estimator or least trimmed squares estimators. For different noise distributions, we present simulations comparing the performance of the proposed algorithm with the standard least squares estimator. The simulated performance is equivalent in the Gaussian noise case and superior when the noise is distributed according to the Laplacian or Cauchy distributions.

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“…Besides Kroonenberg and Van Ginkel [12], other studies about missing data in three-mode data include Hubert et al [34], Louwerse et al [35], and Tian et al [36]. The paper by Kroonenberg and Van Ginkel [12] was aimed at defining combination rules for the Tucker2 model for multiply imputed data sets.…”

Section: Research Questionsmentioning

confidence: 99%

“…However, the problem of accurately taking the threemode structure into account in the imputation model was not addressed (wide imputation was used) and no systematic simulation study was conducted. Hubert et al [34] discussed an EM-based estimation method for the Parafac model that was robust to both outliers and incomplete data. Outliers are not the topic of the present paper so the only EM-based method in our study will be the standard EM algorithm.…”

Section: Research Questionsmentioning

confidence: 99%

Evaluation of multiple-imputation procedures for three-mode component models

Ginkel

Kroonenberg

2017

Journal of Statistical Computation and Simulation

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Three-mode analysis is a generalization of principal component analysis to three-mode data. While two-mode data consist of cases that are measured on several variables, three-mode data consist of cases that are measured on several variables at several occasions. As any other statistical technique, the results of three-mode analysis may be influenced by missing data. Three-mode software packages generally use the expectation-maximization (EM) algorithm for dealing with missing data. However, there are situations in which the EM algorithm is expected to break down. Alternatively, multiple imputation may be used for dealing with missing data. In this study we investigated the influence of eight different multiple-imputation methods on the results of three-mode analysis, more specifically, a Tucker2 analysis, and compared the results with those of the EM algorithm. Results of the simulations show that multilevel imputation with the mode with the most levels nested within cases and the mode with the least levels represented as variables gives the best results for a Tucker2 analysis. Thus, this may be a good alternative for the EM algorithm in handling missing data in a Tucker2 analysis. ARTICLE HISTORY

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Robust PARAFAC for incomplete data

Cited by 34 publications

References 20 publications

Normalization techniques for PARAFAC modeling of urine metabolomic data

Normalization techniques for PARAFAC modeling of urine metabolomic data

Canonical polyadic tensor decomposition in the presence of non Gaussian noise

Evaluation of multiple-imputation procedures for three-mode component models

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