Journal ArticleDOI
The approximation of one matrix by another of lower rank
Carl Eckart,Gale Young +1 more
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In this paper, the problem of approximating one matrix by another of lower rank is formulated as a least-squares problem, and the normal equations cannot be immediately written down, since the elements of the approximate matrix are not independent of one another.Abstract:
The mathematical problem of approximating one matrix by another of lower rank is closely related to the fundamental postulate of factor-theory. When formulated as a least-squares problem, the normal equations cannot be immediately written down, since the elements of the approximate matrix are not independent of one another. The solution of the problem is simplified by first expressing the matrices in a canonic form. It is found that the problem always has a solution which is usually unique. Several conclusions can be drawn from the form of this solution. A hypothetical interpretation of the canonic components of a score matrix is discussed.read more
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Tensor Decompositions and Applications
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A Scaling Method for Priorities in Hierarchical Structures
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Robust principal component analysis
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Principal component analysis
Hervé Abdi,Lynne J. Williams +1 more
TL;DR: Principal component analysis (PCA) as discussed by the authors is a multivariate technique that analyzes a data table in which observations are described by several inter-correlated quantitative dependent variables, and its goal is to extract the important information from the table, to represent it as a set of new orthogonal variables called principal components, and display the pattern of similarity of the observations and of the variables as points in maps.
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The ade4 Package: Implementing the Duality Diagram for Ecologists
TL;DR: The theory of the duality diagram is presented and its implementation in ade4 is discussed, which follows the tradition of the French school of "Analyse des Donnees" and is based on the use of theDuality diagram.