High order Geometric network / Revision 2.1
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Notice
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Copyright (c) 1998- Technion - Israel Inst. of Technology.
In published work, please reference: H. Lipson, H.T. Siegelmann,
1998, "Geometric Neurons", in review
These routines are provided AS IS with no implied warranty
and may be redistributed freely with this notice intact.
For questions, comments and bug reports please contact
merhod@tx.technion.ac.il or iehava@ie.technion.ac.il.
Visit http://tx.technion.ac.il/~merhod to download new versions.

Overview
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This package contains a simple MATLAB implementation of a network
based on geometric neurons - neurons that have a shape
rather than being just points. These neuronscan handle close and
partially overlapping configurations of data
clusters in the input domain, which may be misclassified by classic
network. This is an implementation of a layer of high order neurons,
which take the form of ellipsoids, bananas, and so forth. The net can 
operate both in competitive and in supervised modes. For a full 
description of the theory of this net, print the included postscript
paper.

Installation and use
--------------------

This package contains several MATLAB '.m' files which should be
copied to the same directory in which you have the standard neural
net toolbox installed (e.g. "C:\MATLAB\TOOLBOX\NNET\NNET").
These routines will also work without the neural-net toolbox; just
place them in your working directory. Help will then be available by
typing "HELP function" just like any other MATLAB command.


Demos
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Four demonstration programs are provided. Preferably copy the demo
files (demo*.m and irisdata.dat) into the demonstration directory
(e.g. C:\MATLAB\TOOLBOX\NNET\NNDEMOS).

DEMOG1 - demonstrates the use of competitive ellipsoids in 2D.
DEMOG2 - demonstrates 4th order learning without counter examples
DEMOG3 - demonstrates self-classification of the IrisData in 4D.
DEMOG4 - demonstrates supervised learning of the IrisData, various orders
DEMOG5 - demonstrates competitive learning with high order shapes
DEMOG6 - demonstrates competitive learning with very high order shapes


Functions
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(for detailed help type HELP FUNCTION from within MATLAB)

INITG 		Initialize geometric layer
TRAING 		Train competitive geometric layer
SIMUG		Simulate competitive geometric layer.
NMAPG		Plot contour map of competitive geometric layer
NNGENC2 	Generate random ellipsoidal clusters of data points
NNGENCX 	Generate random clusters of data points
POLYBASE 	Creates high-order symbolic polynomial base functions
EIGTENSR 	Compute high-order eigenstructure of correlation tensor
HIGHCORR 	Gompute high-order homogeneous correlation tensor
HIGHPROD 	High order tensor correlation product
HIGHTRAN 	High order tensor transformation
PERMUTE 	Creates D-order permutations of integers N1..N2
THRESHG		Find percentile threshold of competitive geometric layer





