Copyright: Miguel Equihua (Instituto de Ecología, A.C.)
Citation: This help file was created with Help & Manual (www.ec-software.com).


Fuzzy set clustering options

Standard	Advanced

The options available for fuzzy clustering are listed below.

For each option, the list of possible values for each command are shown within square brackets.

Standard options

•	ANALYSIS [k-means/k-elliptotypes]

•	FUZZYNESS-PARAMETER [decimal value]

•	GROUPS [integer number]

•	NORM [Euclidean/Diagonal]

Advanced options

•	USE [Reciprocal averaging/Original data]

•	TOLERANCE [decimal  value]

•	ZERO

•	ITERATIONS [integer number]


Data file

The structure of the data file is a plain, ASCII document with: (1) one line of data identification, (2) one line stating the numebr of rows and columns, (3) the data block in free format, (4) the alphanumeric labels for the columns and rows.  Each item within a field eight characters long.  If no labels are provided the program will label everything with consecutive digits.  An example file is shown below:

Test data file

7 5

1.0 1.5 0.8 0.0 0.0

0.9 0.8 0.0 1.1 0.0

0   1   1   0   0

0 0 0 1 1

0 0 0 1 0

0 0 1 1 1

0 0 0 0 1

dato 1  dato 2  dato 3  dato 4  dato 5

ind 1   ind 2   ind 3   ind 4   ind 5   ind 6   ind 7


References

Ayyub B. M. y McCuen R.H., 1987.  Quality and uncertainity assesment of wildlife habitat with fuzzy sets.  Journal of Water Resources Planning and Management, 113 (1): 95-109.

Bezdek J.C., 1981. Pattern recognition with fuzzy objective function algorithms. Plenum Press, New York, 256 pp.

Bezdek J.C., 1987. Some non-standard clustering algorithms. In: Legendre P. y Legendre L. (eds.). Developments in numerical ecology (NATO ASI Series Vol. G14), SpringerVerlag, Berlin, Heilderberg.

Bosserman R.W. & Ragade R.K., 1982.  Ecosystems analysis using fuzzy set theory.  Ecological Modelling, 16:191-208.

Roberts D.W., 1986.  Ordination on the basis of fuzzy set theory. Vegetatio, 66:123-131.

McBratney A.B. y Moore A.W., 1985.  Application of fuzzy sets to climatic classification.  Agricultural and Forest Meteorology, 35:165-185.

Kauffmann A., 1975.  Introduction to the theory of fuzzy subsets (Vol. I fundamental theoretical elements).  Academic Press, EUA, 416pp.

Wenger R.B. y Rong Y., 1987.  Two fuzzy set models for comprehensive environmental decision-making.  Journal of Environmental Management, 25:167-180.


Analysis

There are three fuzzy clustering methods that can be applyied with this tools package:

•	k-means

•	k-lines

•	k elliptotype

The default option is k-means.  In order to change the method of analysis use the advanced options window.

When  the k-elliptotypes method is requested, then the parameter alpha will be prompted for.  This parameter especifies the shape of the ellipsoids.  Note that if an alpha value of 1 is supplied the clustering becomes equivalent to another fuzzy clustering options:  fuzzy k-lines method.


Fuzzyness parameter

The parameter takes any real number estrictly larger than 1.   Usually a value of 2 give satisfactory results.  The clustering becomes "harder" as the parameter approches 1 and "fuzzier" as it gets bigger.  The value 1 would produce a hard clustering, but it produces an indetermination in the computation therefore it cannot be used with the fuzzy clustering algorithm.


Norm (shape of clusters)

Basically especifies the kind of distance metric that will be used for cluster construction.

What it does is to set-up the norm inducing matrix that it is use for the computation of distances among individuals.

The euclidean norm is appropiate to represent cluster of a theoretical spheric shape (hyper-spheric in general) and similar size, which implies giving an equivalent weight to each feature.

The diagonal norm is useful when clusters are expected to be, in general, of similar size but features differ in scale of measurement.

No provisions are yet available for the use of a Mahalanobis norm which would assume non spherical and unequal-sized clusters.

Frequently the conservative assumptions associated to the euclidean norm give good results.  Therefore Euclidean is the default setting.  This options can be changed in the advanced options windows.


Groups

This control specifies the number of clusters to fit.  Its parameter is any integer between 2 and 30. The default is 2.


Zero

Whe this option is "on" a fixed cluster centred at "zero" (centroid of zeros) is fitted.  This can be useful  to control the distortion introduced when there are some samples with very few species and/or low abundances.

The default is "off."  It can be changed in the advaced options window.


Maximum number of iterations

Sets the maximum number of iterations trying to achive convergency.  The default value is set to 50.


Tolerance

Specifies the criterion of convergency. Its parameter is any reasonable small positive real.  Usually values between 0.001 and 0.00001 produce good results.  Obviously the largest the value, the shortest the computation time required.


Use options

Allows to choose between an analysis applied to reciprocal averaging axes or to the original co-ordinates.  If reciprocal averaging axes are selected the program will prompt for the number of axes to use.  The default is original data.


Licence

"Fuzzy set clustering tool" produces fuzzy set classifications with the k-means algorithm.

Copyright ©  2001 Miguel Equihua-Zamora

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.

Miguel Equihua-Zamora

equihuam@ecologia.edu.mx

Instituto de Ecologia, A.C.

Apártado Postal 63

km 2.5 antigua carretera a Coatepec

Xalapa, Ver.

Mexico


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