Skinning Analysis of a Mapping Algorithm in Higher Dimensions

Recently, a geometric approach to the coordinatization of measured spaces (called the Map Maker algorithm) was extended to three and high dimensions. This has significance in now allowing a new sort of data projection from higher dimensions to any lower dimension of choice. The algorithms however need a thorough testing review, and this paper makes the necessary thorough analysis of the error and speed performance of the extended approaches. By means of the skinning operation introduced in this paper, we have been able to derive meaningful performance charts with the statistical fluctuations effectively removed. This has resulted in some new findings. We have found that the fit of the data to a given dimensionality is very sensitive to the precision in the given data. In addition, we have resolved a conjecture regarding the dimensionality of the Map Maker algorithm resonating with the dimensionality of the data from which the distance matrix information was derived.