majorization

A partial order over vectors of real numbers

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  • Majorization — This article is about a partial ordering of vectors on Rd. For functions, see Lorenz ordering. In mathematics, majorization is a partial order on vectors of real numbers. For a vector , we denote by the vector with the same components, but sorted …   Wikipedia

  • Stress majorization — is an optimization strategy used in multidimensional scaling (MDS) where, for a set of n , m dimensional data items, a configuration X of n points in r( …   Wikipedia

  • Ingram Olkin — (born July 23, 1924) is a professor emeritus and chair of statistics and education at Stanford University and the Stanford University School of Education. He is known for developing statistical analysis for evaluating policies, particularly in… …   Wikipedia

  • Force-based algorithms — Force based or force directed algorithms are a class of algorithms for drawing graphs in an aesthetically pleasing way. Their purpose is to position the nodes of a graph in two dimensional or three dimensional space so that all the edges are of… …   Wikipedia

  • Karamata's inequality — In mathematics, Karamata s inequality, also known as the Majorization Inequality, states that if f(x) is a convex function in x and the sequence :x 1, x 2, ..., x n majorizes:y 1, y 2, ..., y n then :f(x 1)+f(x 2)+...+f(x n) ge f(y 1)+f(y… …   Wikipedia

  • Dominance order — Example of dominance ordering of partitions of n. Here, n = 6, nodes are partitions of 6, edges indicate that the upper node dominates the lower node. While this particular partial ordering is graded, this is not true for the dominance ordering… …   Wikipedia

  • Douglas' lemma — In operator theory, an area of mathematics, Douglas lemma relates factorization, range inclusion, and majorization of Hilbert space operators. It is generally attributed to Ronald G. Douglas, although Douglas acknowledges that aspects of the… …   Wikipedia

  • Nonlinear dimensionality reduction — High dimensional data, meaning data that requires more than two or three dimensions to represent, can be difficult to interpret. One approach to simplification is to assume that the data of interest lies on an embedded non linear manifold within… …   Wikipedia

  • Multidimensional scaling — (MDS) is a set of related statistical techniques often used in information visualization for exploring similarities or dissimilarities in data. MDS is a special case of ordination. An MDS algorithm starts with a matrix of item–item similarities,… …   Wikipedia

  • List of numerical analysis topics — This is a list of numerical analysis topics, by Wikipedia page. Contents 1 General 2 Error 3 Elementary and special functions 4 Numerical linear algebra …   Wikipedia

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