EXAMPLE E

TITLE= Illustrating the Problem of Local Minima (Cox and Cox Data)
SUBTITLE= This example shows that a solution can be wrong about half of the time for some problems.

Nobjects=12
DissimilarityList
0
0.099	0
0.033	0.022	0
0.183	0.114	0.042	0
0.148	0.224	0.059	0.068	0
0.198	0.039	0.053	0.085	0.051	0
0.462	0.266	0.322	0.435	0.268	0.025	0
0.628	0.442	0.444	0.406	0.240	0.129	0.014	0
0.113	0.070	0.046	0.047	0.034	0.002	0.106	0.129	0
0.173	0.119	0.162	0.331	0.177	0.039	0.089	0.237	0.071	0
0.434	0.419	0.339	0.505	0.469	0.390	0.315	0.349	0.151	0.430	0
0.762	0.633	0.781	0.700	0.758	0.625	0.469	0.618	0.440	0.538	0.607	0

STARTMDSAnalysisTypeNum=4
STARTBadnessFunctionNum=1
STARTDistanceFunctionNum=0
STARTDimensionsNum=2


This problem is taken from in a draft paper by Cox and Cox, available on the Internet at
http://www.ncl.ac.uk/mds/

Cox and Cox use this test case to illustrate the dangers of not understanding
the frequent occurrence of 'solutions' being due to local minima.  They
also note that the SPSS manual gives bad advice on this topic.

Cox and Cox get Stress1=9.39% using a slightly different ordinal procedure 
than that used by PERMAP.  PERMAP (centering indifferent) gets Stress1=9.47% about 
half the time and is trapped in a local minima the other half of the time.  Use the 
Auto Stop and Auto Repeat options to monitor the frequency of finding the best solution.
