Body diagonalization of core matrices in three‐way principal components analysis: Theoretical bounds and simulation

Henrion, René

doi:10.1002/cem.1180070604

Cited by 34 publications

(17 citation statements)

References 12 publications

(7 reference statements)

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“…If not removed, this error would account for the major amount of variation. Three-way PCA, based on the Tucker-3 model [39][40][41][42][43][44][45], has been used for the identification of classes of samples present in the two datasets. Three-way PCA allows the three-way structure of the dataset which can be considered as a parallelepiped of size I x J x K (conventionally defined as objects, variables and conditions), where, in our case: I is the number of rows of the grid (the x coordinates, i.e.…”

Section: Home-made Approaches: Three-way Pcamentioning

confidence: 99%

Numerical approaches for quantitative analysis of two‐dimensional maps: A review of commercial software and home‐made systems

et al. 2005

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The present review attempts to cover a number of methods that have appeared in the last few years for performing quantitative proteome analysis. However, due to the large number of methods described for both electrophoretic and chromatographic approaches, we have limited this review to conventional two-dimensional (2-D) map analysis which couples orthogonally a charge-based step (isoelectric focusing) to a size-based separation step (sodium dodecyl sulfateelectrophoresis). The first and oldest method applied to 2-D map data reduction is based on statistical analysis performed on sets of gels via powerful software packages, such as Melanie, PDQuest, Z3 and Z4000, Phoretix and Progenesis. This method calls for separately running a number of replicas for control and treated samples. The two sets of data are then merged and compared via a number of software packages which we describe. In addition to commerciallyavailable systems, a number of home made approaches for 2-D map comparison have been recently described and are also reviewed. They are based on fuzzyfication of the digitized 2-D gel image coupled to linear discriminant analysis, three-way principal component analysis or a combination of principal component analysis and soft-independent modeling of class analogy. These statistical tools appear to perform well in differential proteomic studies.

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Section: Home-made Approaches: Three-way Pcamentioning

confidence: 99%

Numerical approaches for quantitative analysis of two‐dimensional maps: A review of commercial software and home‐made systems

et al. 2005

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“…Kiers provides a method for doing so in References [13,14]. Also see References [15,16]. If the core can be simplified then adjust the individual score and Y Y-loadings arrays and replaceM ÂÑÂA D A by the simpler core.…”

Section: N-pls and Mrplsmentioning

confidence: 98%

Regression with multiple regressor arrays

Plaehn

Lundahl

2007

Journal of Chemometrics

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Extension of standard regression to the case of multiple regressor arrays is given via the Kronecker product. The method is illustrated using ordinary least squares regression (OLS) as well as the latent variable (LV) methods principal component regression (PCR) and partial least squares regression (PLS). Denoting the method applied to PLS as mrPLS, the latter was shown to explain as much or more variance for the first LV relative to the comparable L-partial least squares regression (L-PLS) model. The same relationship holds when mrPLS is compared to PLS or n-way partial least squares (N-PLS) and the response array is 2-way or 3-way, respectively, where the regressor array corresponding to the first mode of the response array is 2-way and the second mode regressor array is an identity matrix. In a comparison with N-PLS using fragrance data, mrPLS proved superior in a validation sense when model selection was used. Though the focus is on 2-way regressor arrays, the method can be applied to n-way regressors via N-PLS.

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“…More typically, an alternating least squares (ALS) approach is used for the computation; see [26,45,121. The Tucker decomposition is not unique, but measures can be taken to correct this [19,20,21,461. Observe that the right-hand-side of (4) is a Tucker tensor, to be discussed in more detail in 54.…”

Section: Tensor Decompositionsmentioning

confidence: 99%