# Documentation of sammon

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## Function Synopsis

`[DataLow, Sstress, PCAinit] = sammon(DataHigh, SamOpt, Labels, DataLowStart)`

## Help text

``` Multidimensional scaling (SAMMON mapping)

This function performs SAMMON mapping, a multidimensional
scaling (MDS) method used for scaling multidimensional data
to a lower dimension (normally to two or three dimensions).
The scaled data give an abstract picture of the multi-
dimensional data.
When no optimization function (optimization toolbox) is available
a classical scaling method is used (producing good results as well).

Syntax:  [DataLow, Sstress, PCAinit] = sammon(DataHigh, SamOpt, Labels, DataLowStart)

Input parameter:
DataHigh  - Matrix of multidimensional data
every row corresponds to one multidimensional
data point

SamOpt    - Vector containing options for sammon mapping
SamOpt(1): SplitCoef - Split coefficient, scalar in [0.5  1]
which percentage of the data points is used for direct MDS,
the remaining part is added later; for many data points this
speeds up the MDS - trading against less accurate results
1: exact sammon algorithm with all data points (standard)
<1: faster mapping producing a not so accurate result
only used with more than 100 data points
SamOpt(2): DimDataLow - dimension of low dimensional data
DimDataLow: [ 1 2 3 ... ]
if omitted or NaN, DataLowDim = 2 is assumed
SamOpt(3): DoSamPlot - scalar indicating plotting of results
0: no plot
1+: plot results (when low dimension is 2D or 3D)
for each distinc number a new figure is opened or
the figure with this number is reused
SamOpt(4): DoRandInit - initialization of low-dimensional data
0: pca (principal component analysis)
1: random initialization (uniform at random)
(Cox&Cox bzw. Borg/Groenen) see below

Labels     - Matrix containing strings used for labeling data points
if empty, no labels are plotted
if NaN, row number of data points are used
if less labels are provided than points, omitted
labels are produced using row number of data points

DataLowStart- Matrix of initial low dimensional data
if empty random values are generated or PCA-initialization is used

Output parameter:
DataLow   - Matrix of lowdimensional data
every row corresponds to one lowdimensional
data point and corresponds with DataHigh

Sstress   -

PCAinit   -

References:
J.W. Sammon: A nonlinear Mapping for Data Structure Analysis. IEEE Trans. on Computers, 18, 401-409, 19??.
Ingwer Borg and Patrick Groenen: Modern Multidimensional Scaling. Springer, New York, 1997.
Trevor F. Cox and Michael A.A. Cox: Multidimensional Scaling. Chapman&Hall, London 1994.
```

## Cross-Reference Information

This function calls This function is called by
 GEATbx: Main page  Tutorial  Algorithms  M-functions  Parameter/Options  Example functions  www.geatbx.com

This document is part of version 3.8 of the GEATbx: Genetic and Evolutionary Algorithm Toolbox for use with Matlab - www.geatbx.com.
The Genetic and Evolutionary Algorithm Toolbox is not public domain.