High Quality Content by WIKIPEDIA articles! 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(<<m)-dimensional space is sought that minimises the so called stress function ?(X). Usually r is 2 or 3, i.e. the rtimes n matrix X lists points in 2- or 3-dimensional Euclidean space so that the result may be visualised (i.e. an MDS plot). The function ? is a loss or cost function that measures the squared differences between ideal (m-dimensional) distances and actual distances in r-dimensional space. It is defined as: sigma(X)=sum_{i<jle n}w_{ij}(d_{ij}(X)-delta_{ij})^2 where w_{ij}ge 0 is a weight for the measurement between a pair of points (i,j), dij(X) is the euclidean distance between i and j and ?ij is the ideal distance between the points (their separation) in the m-dimensional data space.

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