sammonm

SAMMONM

Sammon mapping

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

Input
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

Output
W Trained mapping
D K-dimensional dataset

Description

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.

Example(s)

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

Reference(s)

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]