An Examination Of Some Factors Related To Using Different Minkowski Models In Non-Metric Multidimensional Scaling

Area of Science:

• Data analysis and computational statistics.
• Multidimensional scaling techniques.

Background:

• Non-metric multidimensional scaling (NMDS) is widely used, leading to the development of various computer programs.
• Understanding the impact of different metric models on NMDS solution accuracy is crucial for reliable data interpretation.

Purpose of the Study:

• To investigate the effect of using different metric models on the accuracy of non-metric multidimensional scaling solutions.
• To compare the performance of three NMDS programs: MDSCAL-5M, TORSCA-9, and POLYCON-II.

Main Methods:

• Generated data under five different metrics.
• Analyzed the generated data using MDSCAL-5M, TORSCA-9, and POLYCON-II, recovering solutions under all five metrics.
• Evaluated the 'stress' values to determine solution accuracy.

Main Results:

• POLYCON-II demonstrated the highest accuracy among the tested programs, though overall success was limited.
• The Euclidean metric generally provided the best or near-best recovery, irrespective of the metric used to generate the original data.
• Different Minkowski metrics showed high similarity in ranking dissimilarity data.

Conclusions:

• The choice of metric in non-metric multidimensional scaling warrants careful consideration.
• While POLYCON-II showed superior performance, the Euclidean metric appears robust for recovery across various data generation metrics.
• The similarity in dissimilarity ranking among Minkowski metrics suggests some flexibility in metric selection for NMDS.