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TOOLS > SCALING/DECOMPOSITION > NON-METRIC MDS

PURPOSE Non-metric multidimensional scaling of a proximity matrix.

DESCRIPTION Given a matrix of proximities (similarities or dissimilarities) among a set of items, program finds a set of points in k-dimensional space such that the Euclidean distances among these points corresponds as closely as possible to a rank preserving transformation of the input proximities. The algorithm is based on the MDS(X) MINISSA program.

PARAMETERS
Input dataset
Name of file containing proximity matrix. Data type: Square symmetric matrix.

No of dimensions: (Default = 2)
Number of dimensions to use in representing items in Euclidean space.

Similarities or Dissimilarities?  (Default = Similarities)
Whether the data represent similarities or dissimilarities.  If similarities, large values of X(i,j) will draw i and j close together on the MDS map.  If dissimilarities, large values will push i and j apart on the map.

Starting Configuration: (Default = Torsca)
How to generate initial location of points in space.
Choices are:

Metric - Performs Gower's classical metric ordination procedure.

Torsca - Uses principal components of rank-order data.

File - Reads starting coordinates from UCINET dataset.

Random - Locates points randomly in space.

Starting Config Filename
Name of the coordinate dataset if the file option is chosen . This UCINET dataset should consist of an nxk matrix of values. Each column corresponds to the co-ordinates in each of the dimensions specified. Hence row i gives the co-ordinates of the ith point.

Print Diagnostics (Default = No)
If Yes is selected then dyads with large discrepancies between the proximity data and the plot distances will be printed.

Output dataset: (Default = 'NonMetricMdsCoord')
Name of file containing the co-ordinates of the points in Euclidean space.

LOG FILE The output consists of a log file and a scatterplot viewed in the scatter plot viewer. The viewer gives a 2D scatterplot of the first pair of co-ordinates, the x-axis is the first co-ordinate set and the y-axis is the second. If the number of dimensions selected was greater than two then any pair of dimensions can be plotted by selecting them in the x-axis and y-axis drop down boxes. If the dataset had multiple levels then other levels can be viewed by selecting the required level in the matrix box. The scatterplot can be saved or printed and previously stored plots can also be opend. The labels can be turned on or off or resized using the options on the right hand side. Clicking on the arrows allow the plot to be flipped in the horizontal or vertical axis. The points can also be turned on or off. The label positions can be moved away from the points in an upward direction by increasing the value in the box headed Label Pos:, the margins can also be increased or decreased and the plots can be centred if required. Clicking on the axes scales displays the values on the x and y axes. Individual points (with their labels) can be moved by left clicking and then dragging them to the required position. The original mds plot positions can be restored by clicking the R button. the text log file is a  numeric display of coordinates of each point in space together with information about the stress.

TIMING O(N^4)

COMMENTS MDS solutions are not unique, and they are subject to convergence to local minima.  The first point means that two or more maps can be equally good (same stress) but place points in radically different locations. The second point means that it is possible for the algorithm to fail to find the configuration with least stress.  If you suspect this has happened, run the program several times using random starting configurations. Stress values below 0.1 are excellent and above 0.2 unacceptable.

REFERENCES Kruskal J B and Wish M (1978).  Multidimensional Scaling, Newbury Park: Sage Publications.

Kruskal J B (1964).  Multidimensional Scaling by optimizing goodness-of-fit to a non-metric hypothesis.  Psychometrika 29, 1-27.