N-way principal component analysis theory, algorithms and applications

Henrion, René

doi:10.1016/0169-7439(93)e0086-j

Cited by 169 publications

(75 citation statements)

References 36 publications

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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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“…Tensor decomposition was studied in psychometric data analysis during the 1960s, when data sets having more than two dimensions (generally called "three-way data sets") became widely used [17]. A fundamental achievement was brought by Tucker (1963), who proposed to decompose a 3-D signal using directly a 3-D principal component analysis (PCA) instead of unfolding the data on one dimension and using the standard SVD.…”

Section: Higher Order Svdmentioning

confidence: 99%

Higher Order SVD Analysis for Dynamic Texture Synthesis

Costantini

Sbaiz

Süsstrunk

2008

IEEE Trans. on Image Process.

114

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Abstract-Videos representing flames, water, smoke, etc., are often defined as dynamic textures: "textures" because they are characterized by the redundant repetition of a pattern and "dynamic" because this repetition is also in time and not only in space. Dynamic textures have been modeled as linear dynamic systems by unfolding the video frames into column vectors and describing their trajectory as time evolves. After the projection of the vectors onto a lower dimensional space by a singular value decomposition (SVD), the trajectory is modeled using system identification techniques. Synthesis is obtained by driving the system with random noise. In this paper, we show that the standard SVD can be replaced by a higher order SVD (HOSVD), originally known as Tucker decomposition. HOSVD decomposes the dynamic texture as a multidimensional signal (tensor) without unfolding the video frames on column vectors. This is a more natural and flexible decomposition, since it permits us to perform dimension reduction in the spatial, temporal, and chromatic domain, while standard SVD allows for temporal reduction only. We show that for a comparable synthesis quality, the HOSVD approach requires, on average, five times less parameters than the standard SVD approach. The analysis part is more expensive, but the synthesis has the same cost as existing algorithms. Our technique is, thus, well suited to dynamic texture synthesis on devices limited by memory and computational power, such as PDAs or mobile phones.

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“…This is accomplished with the Tucker-3 design (Henrion, 1994;Tucker, 1966). Thereby, complete X factorization can be obtained either by direct decomposition (Eq.…”

Section: Tucker-3 Modelmentioning

confidence: 99%

Model identification in presence of incomplete information by generalized principal component analysis: Application to the common and differential responses of Escherichia coli to multiple pulse perturbations in continuous, high‐biomass density culture

Guebel¹,

Cánovas

Torres

2009

Biotech & Bioengineering

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In a previous report we described a multivariate approach to discriminate between the different response mechanisms operating in Escherichia coli when a steady, continuous culture of these bacteria was perturbed by a glycerol pulse (Guebel et al., 2009, Biotechnol Bioeng 102: 910-922). Herein, we present a procedure to extend this analysis when multiple, spaced pulse perturbations (glycerol, fumarate, acetate, crotonobetaine, hypersaline plus high-glycerol basal medium and crotonobetaine plus hypersaline basal medium) are being assessed. The proposed method allows us to identify not only the common responses among different perturbation conditions, but to recognize the specific response for a given stimulus even when the dynamics of the perturbation is unknown. Components common to all conditions are determined first by Generalized Principal Components Analysis (GPCA) upon a set of covariance matrices. A metrics is then built to quantify the similitude distance. This is based on the degree of variance extraction achieved for each variable along the GPCA deflation processes by the common factors. This permits a cluster analysis, which recognizes several compact sub-sets containing only the most closely related responsive groups. The GPCA is then run again but is restricted to the groups in each sub-set. Finally, after the data have been exhaustively deflated by the common sub-set factors, the resulting residual matrices are used to determine the specific response factors by classical principal component analysis (PCA). The proposed method was validated by comparing its predictions with those obtained when the dynamics of the perturbation was determined. In addition, it showed to have a better performance than the obtained with other multivariate alternatives (e.g., orthogonal contrasts based on direct GPCA, Tucker-3 model, PARAFAC, etc.).

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N-way principal component analysis theory, algorithms and applications

Cited by 169 publications

References 36 publications

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

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

Higher Order SVD Analysis for Dynamic Texture Synthesis

Model identification in presence of incomplete information by generalized principal component analysis: Application to the common and differential responses of Escherichia coli to multiple pulse perturbations in continuous, high‐biomass density culture

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