Sammon's projection

Sammon's projection

Sammon's projection, or Sammon's mapping is an algorithm that maps a high-dimensional space to a space of lower dimensionality (see multidimensional scaling).

Denote the distance between ith and jth objects in the original space by scriptstyle d^{*}_{ij}, and the distance between their projections by scriptstyle d^{}_{ij}. Sammon's projection aims to minimize the following error function, which is often referred to as Sammon's stress:

:E = frac{1}{sumsum_{isumsum_{i.

The minimization can be performed either by gradient descent, as proposed initially, or by other means.

oftware

Sammon's projection is supported by [http://www.r-project.org/ R] (package MASS) and by [http://www.cis.hut.fi/projects/somtoolbox/ SOM toolbox] , a free functional package for Matlab.

Bibliography

*J. W. Sammon, Jr. "A nonlinear mapping for data structure analysis". "IEEE Transactions on Computers", 18, pp. 401–409, 1969.


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