Dissimilarity: To Configuration (i-spline mds)...

A command that creates a Configuration object from a Dissimilarity object.

Dissimilarities δij and disparities dij will be related by a spline function:

dij = ∑k=1..(numberOfInteriorKnots+order) splinek (knots, order, δij),

where splinek (·) is the value of the kth I-spline of order order and knot sequence knot evaluated at δij.

Settings

Number of dimensions
determines the dimensionality of the configuration.
Number of interior knots
determines the number of segment boundaries. Each interior knot is the boundary between two segments. The splines in each segment will be joined as continuously as possible.
Order of I-spline
The order of the polynomial basis of the I-spline.

Finding the optimal Configuration involves a minimization process:

Tolerance
When successive values for the stress differ by less than Tolerance, the minimization process stops.
Maximum number of iterations
Minimization stops after this number of iterations has been reached.
Number of repetitions
If chosen larger than 1, the minimization process will be repeated, each time with another random start configuration. The configuration that results in minimum stress, will be saved.

Hints

If numberOfInteriorKnots is zero, polynomial regression will be performed. Therefore , the combination numberOfInteriorKnots = 0 and order = 1 also gives interval scaling (in fact, it is the implementation in this program).

In the limit when order = 0 and numberOfInteriorKnots = numberOfDissimilarities, monotone regression is performed.

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© djmw, April 7, 2004