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

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.

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