Package com.imsl.test.example.stat

Class MultidimensionalScalingEx1

java.lang.Object

com.imsl.test.example.stat.MultidimensionalScalingEx1

public class MultidimensionalScalingEx1
extends Object

Applies multidimensional scaling to a distance matrix.

The following example concerns some intercity distance rankings. The data are described by Young and Lewyckyj (1979, page 83). The driving mileages between various cities in the United States are ranked, yielding a symmetric ordinal dissimilarity matrix. These rankings are used as input to class MultidimensionalScaling. A Euclidean model is fit. The resulting two-dimensional scaling yields results closely resembling the locations of the major cities in the U.S. Note that MultidimensionalScaling assumes continuous, not ranked, data.

The original rankings are given as: $$\begin{pmatrix} - & 4 & 22 & 8 & 34 & 6 & 10 & 35 & 36 & 3\\ & - & 13 & 15 & 31 & 21 & 9 & 32 & 30 & 5\\ & & - & 12 & 11 & 29 & 27 & 16 & 19 & 26\\ & & & - & 24 & 18 & 25 & 28 & 33 & 23\\ & & & & - & 39 & 42 & 2 & 17 & 37\\ & & & & & - & 20 & 44 & 45 & 14\\ & & & & & & - & 43 & 40 & 1\\ & & & & & & & - & 7 & 41\\ & & & & & & & & - & 38\\ & & & & & & & & & -\\ \end{pmatrix} $$

References

1. Young, Forrest W., and Rostyslaw Lewyckyj (1979), ALSCAL-4 Users Guide, second edition, Data Analysis and Theory Associates, Chapel Hill, North Carolina.

See Also:

• Code
• Output

Constructor Summary

Constructors

Constructor	Description
MultidimensionalScalingEx1()

Method Summary

Modifier and Type	Method	Description
static void	main(String[] args)

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details

MultidimensionalScalingEx1

public MultidimensionalScalingEx1()

Method Details

main

public static void main(String[] args)
                 throws Exception

Throws:

Exception