This survey provides an overview of higher-order tensor decompositions, their applications, and available software. A tensor is a multidimensional or $N$-way array. Decompositions of higher-order tensors (i.e., $N$-way arrays with $N \geq 3$) have applications in psycho-metrics, chemometrics, signal processing, numerical linear algebra, computer vision, numerical analysis, data mining, neuroscience, graph analysis, and elsewhere. Two particular tensor decompositions can be considered to be higher-order extensions of the matrix singular value decomposition: CANDECOMP/PARAFAC (CP) decomposes a tensor as a sum of rank-one tensors, and the Tucker decomposition is a higher-order form of principal component analysis. There are many other tensor decompositions, including INDSCAL, PARAFAC2, CANDELINC, DEDICOM, and PARATUCK2 as well as nonnegative variants of all of the above. The N-way Toolbox, Tensor Toolbox, and Multilinear Engine are examples of software packages for working with tensors.

/pdf/tensor-decompositions-and-applications-46vl2ih5gn.pdf

Tensor Decompositions and Applications

Two-way arrays or matrices are often not enough to represent all the information in the data and standard two-way analysis techniques commonly applied on matrices may fail to find the underlying structures in multi-modal datasets. Multiway data analysis has recently become popular as an exploratory analysis tool in discovering the structures in higher-order datasets, where data have more than two modes. We provide a review of significant contributions in the literature on multiway models, algorithms as well as their applications in diverse disciplines including chemometrics, neuroscience, social network analysis, text mining and computer vision.

/pdf/unsupervised-multiway-data-analysis-a-literature-survey-2fs9anhe18.pdf

Unsupervised Multiway Data Analysis: A Literature Survey

http://libpls.net/publication/MCUVE_2008.pdf

A variable selection method based on uninformative variable elimination for multivariate calibration of near-infrared spectra

Some forty years ago, when geotechnical centrifuge modelling had been rediscovered and was being developed once more after the early work of Phillips (1869), only a few studies were devoted to the questions and concerns about scaling laws and similitude conditions. During the first decades, it was relatively easy for researchers to keep themselves informed about the main outcomes of these studies and to take them into account when designing new centrifuge model tests. This is obviously not true today following the welcome growth in terms of the large number of centrifuge facilities now in operation around the world. It is increasingly difficult, but yet absolutely essential, to know about the relevant developments concerning studies into the scaling laws and, furthermore, into the limits of the domains of the use of centrifuge modelling. On the other hand, new media offers a significant opportunity to provide this resource to the physical modelling community. New topics are investigated by many researcher...

Catalogue of scaling laws and similitude questions in geotechnical centrifuge modelling

Fast, comprehensive two-dimensional liquid chromatography.

The capacity of surface foundations on clay under pure vertical (V), horizontal (H) or moment (M) loading may be expressed in non-dimensional form through the use of appropriate bearing capacity factors, with values that will be affected by the shape of the foundation and also any variation of undrained shear strength with depth. A common assumption has then been that the shape of the complete failure envelope in three-dimensional loading space (V, M, H) will be similar regardless of foundation shape and soil non-homogeneity, once scaled to the appropriate apex points. The appropriateness of this assumption has been explored by means of two- and three-dimensional finite element analyses of strip and circular footings, for a simple Tresca soil model where the shear strength varies linearly with depth. With a view to applications involving partially embedded foundations, such as offshore skirted foundations, full suction and ‘bonding’ with the underlying soil has been assumed. The paper documents the normal...

Effect of strength non-homogeneity on the shape of failure envelopes for combined loading of strip and circular foundations on clay

Introduction The Offshore Environment Offshore Site Investigation Soil Behaviour Piled Foundations Shallow Foundations Anchoring Systems Mobile Drilling Rigs Pipeline and Riser Geotechnics Geohazards

Offshore Geotechnical Engineering

Results of a finite element study addressing the effect of embedment on the undrained bearing capacity of shallow strip foundations under uniaxial and combined loading are reported. Uniaxial vertical (V), moment (M) and horizontal (H) capacity and combined VH, VM and general VMH capacity are assessed. Ultimate limit states and the kinematic mechanisms accompanying failure are presented. Ultimate limit states under combined loading are presented as failure envelopes expressed in terms of loads non-dimensionalised by the foundation geometry and soil undrained shear strength and loads normalised by the ultimate uniaxial limit load, in order to describe their size and shape respectively. The results presented in this paper show that the size and shape of failure envelopes defining the undrained capacity of shallow foundations under general loading are dependent on embedment ratio.

Effect of embedment on the undrained capacity of shallow foundations under general loading

Recent advances in offshore geotechnics for deep water oil and gas developments

Three-dimensional failure envelopes can be used to define the bearing capacity and proximity to failure of shallow foundations under general vertical, horizontal and moment loading (V, H, M/B). Different structures, and different load cases for the same structure, cover varying domains of (±V, ±H, ±M/B) load space; therefore, a fully encompassing failure envelope in (V, H, M/B) load space is a useful tool to define ultimate limit states for design. In this technical note, a closed-form expression is proposed that enables prediction of undrained bearing capacity of skirted foundations under general in-plane loading, valid for a range of embedment ratios and soil shear strength heterogeneities.

Susan Gourvenec

Papers

Effect of strength non-homogeneity on the shape of failure envelopes for combined loading of strip and circular foundations on clay

Offshore Geotechnical Engineering

Effect of embedment on the undrained capacity of shallow foundations under general loading

Recent advances in offshore geotechnics for deep water oil and gas developments

Undrained failure envelope for skirted foundations under general loading