Dear Iza Korsmit

For mapping a 3D physical space into a 2D plane, the best MDS strategy is the direct orthogonal projection (see the image attached). But this is the case for physical objects, where the measure is to minimize the Euclidean norm , to render the best distance-preserving representation as ||pi-pj|| ≈ dij. For the case of the physical example illustrated in the image, we can perfectly expect this representation to fulfill, because they are quantizable. Whereas, for some statistical analyses, such real environment cannot be imagined in mind, and the space might be high-dimensional. In such a case you may define a performance measure (norm), for the data-set and try to find which of the possible representations renders the best expectation (minimum norm)? This is how you can compare them together.

For statistical analyses, as comparing the voting turn-out for various volunteers, some quantities are available to be quantized, however, sometimes the preference is to be analyzed in a poll, and preference is not exactly quantizable. An alternative to quantize the preferences, could might be the Fuzzy Logic.

Look the WikiPedia page:

https://en.wikipedia.org/wiki/Multidimensional_scaling

which redirects more info on preference strategy in MDS, to:

https://en.wikipedia.org/wiki/Perceptual_mapping

Hope it would be helpful.

You can try mapping

Dear Iza Korsmit,

Please check links and attached files

https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.92.6337&rep=rep1&type=pdf

https://arxiv.org/ftp/arxiv/papers/1103/1103.3863.pd

Article Research note: A multidimensional scaling comparison of colo...

Best regards