THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

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

On robust estimation of the location parameter

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Principles Of Fluorescence Spectroscopy

https://www.cs.cmu.edu/~pmuthuku/mlsp_page/lectures/Parafac.pdf

PARAFAC. Tutorial and applications

A sub-fraction of dissolved organic matter fluoresces when excited with ultraviolet light. This property is used to quantify and characterize changes in dissolved organic matter (DOM) in aquatic environments. Detailed mapping of the fluorescence properties of DOM produces excitation emission matrices (EEM), which are well suited to multi-way data analysis techniques (chemometrics). Techniques such as parallel factor analysis (PARAFAC) are increasingly being applied to characterize DOM fluorescence properties. Here, an introduction to the technique and description of the advantages and pitfalls of its application to DOM fluorescence is presented. Additionally a MATLAB based tutorial and toolbox specific to PARAFAC analysis of DOM fluorescence is presented.

https://aslopubs.onlinelibrary.wiley.com/doi/epdf/10.4319/lom.2008.6.572

Characterizing dissolved organic matter fluorescence with parallel factor analysis: a tutorial

Tracing dissolved organic matter in aquatic environments using a new approach to fluorescence spectroscopy

Principal component analysis is one of the most important and powerful methods in chemometrics as well as in a wealth of other areas. This paper provides a description of how to understand, use, and interpret principal component analysis. The paper focuses on the use of principal component analysis in typical chemometric areas but the results are generally applicable.

/pdf/principal-component-analysis-1sba76ou47.pdf

Principal component analysis

PARAllel FACtor analysis (PARAFAC) is increasingly used to decompose fluorescence excitation emission matrices (EEMs) into their underlying chemical components. In the ideal case where fluorescence conforms to Beers Law, this process can lead to the mathematical identification and quantification of independently varying fluorophores. However, many practical and analytical hurdles stand between EEM datasets and their chemical interpretation. This article provides a tutorial in the practical application of PARAFAC to fluorescence datasets, demonstrated using a dissolved organic matter (DOM) fluorescence dataset. A new toolbox for MATLAB is presented to support improved visualisation and sensitivity analyses of PARAFAC models in fluorescence spectroscopy.

/pdf/fluorescence-spectroscopy-and-multi-way-techniques-parafac-4p2u0gs62q.pdf

Rasmus Bro

Papers

PARAFAC. Tutorial and applications

Characterizing dissolved organic matter fluorescence with parallel factor analysis: a tutorial

Tracing dissolved organic matter in aquatic environments using a new approach to fluorescence spectroscopy

Principal component analysis

Fluorescence spectroscopy and multi-way techniques. PARAFAC