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Sammon mapping

    W = A*SAMMONM([],K,MAX)
    D = B*W

 A Dataset, used for training the mapping
 B Dataset, same dimensionality as A, to be mapped
 K Target dimension of mapping (default 2)
 MAX Maximum number of iterations, default 100

 W Trained mapping
 D K-dimensional dataset


This is a simplified interface to the more complex MDS routine for high  dimensional data visualisation. The output is a non-linear projection of  the original vector space to a K-dimensional target space.

The main differences with MDS are that SAMMONM operates on feature based  datasets, while MDS expects dissimilarity matrices; MDS maps new objects  by a second optimisation procedures minimizing the stress for the test  objects, while SAMMONM uses a linear mapping between dissimilarities and  the target space. See also PREX_MDS for examples. A different procedure  for the same purpose is TSNEM.


 prdatasets;            % make sure prdatasets is in the path
 a = satellite;         % 36D dataset, 6 classes, 6435 objects
 [x,y] = gendat(a,0.5); % split in train and test set
 w = x*sammonm;         % compute mapping
 figure; scattern(x*w); % show trainset mapped to 2D: somewhat overtrained
 figure; scattern((x+randn(size(x))*1e-5)*w): % some noise helps
 figure; scattern(y*w); % show test set mapped to 2D


1. JW Sammon Jr A nonlinear mapping for data structure analysis,  IEEE Transactions on Computers C-18, pp. 401-409,1969.
2. E. Pekalska, D. de Ridder, R.P.W. Duin, and M.A. Kraaijveld, A new method of generalizing Sammon mapping with application to algorithm speed-up, ASCI99, Proc. 5th Annual ASCI Conf., 1999, 221-228. [pdf]

See also

datasets, mappings, pcam, mds, tsnem, prex_mds, scatterd, scattern,

PRTools Contents

PRTools User Guide

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