Dissimilarity: To Configuration (ispline mds)...


A command that creates a Configuration object from a Dissimilarity object.
Dissimilarities δ_{ij} and disparities d′_{ij} will be related by a spline function:
d′_{ij} = ∑_{k=1..(numberOfInteriorKnots+order)} spline_{k} (knots, order, δ_{ij}), 
where spline_{k} (·) is the value of the k^{th} Ispline of order order and knot sequence knot evaluated at δ_{ij}.
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 Ispline

The order of the polynomial basis of the Ispline.
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