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   - 

 see also: samplot, samadd

 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