Sammon mapping in Python

Date: 18 April 2014

sammontest.py

Run sammontest.py() with no arguments to test sammon.py on Fisher's iris dataset. You should get an output image as the one shown below:

sammon.py

Simple python implementation of Sammon's non-linear mapping algorithm [1]. Perform Sammon mapping on dataset x

y = sammon(x) applies the Sammon nonlinear mapping procedure on multivariate data x, where each row represents a pattern and each column represents a feature. On completion, y contains the corresponding co-ordinates of each point on the map. By default, a two-dimensional map is created. Note if x contains any duplicated rows, SAMMON will fail (ungracefully).

[y,E] = sammon(x) also returns the value of the cost function in E (i.e. the stress of the mapping).

An N-dimensional output map is generated by y = sammon(x,n) .

A set of optimisation options can be specified using optional arguments, y = sammon(x,n,[OPTS]):

• maxiter - maximum number of iterations
• tolfun - relative tolerance on objective function
• maxhalves - maximum number of step halvings
• input - {'raw','distance'} if set to 'distance', X is interpreted as a matrix of pairwise distances.
• display - 0 to 2. 0 least verbose, 2 max verbose.
• init - {'pca', 'random'}

The default options are retrieved by calling sammon(x) with no parameters.

Authors

Tom J. Pollard (https://twitter.com/tompollard)

Ported from MATLAB implementation by Gavin C. Cawley and Nicola L. C. Talbot

References

[1] Sammon, John W. Jr., "A Nonlinear Mapping for Data Structure Analysis", IEEE Transactions on Computers, vol. C-18, no. 5, pp 401-409, May 1969.

Copyright

Copyright : (c) Dr Gavin C. Cawley, November 2007.

This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA