Dimensionality reduction & clustering / NMDS
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NMDS preserves only the rank order of distances: points close together are similar under the chosen distance. The axes have no variance-explained percentage; coordinates are rescaled so that ordination distances match the dissimilarities in overall size (stress is unaffected by scaling).
Kruskal stress measures how well the plot matches the ranked distances: < 0.05 excellent, < 0.1 good, < 0.2 fair, ≥ 0.2 interpret with caution (rule of thumb after Clarke 1993).
The Shepard plot shows observed dissimilarity against ordination distance, with the monotone fit in red; the closer the points lie to the line, the lower the stress.
NMDS is iterative and depends on the starting configuration: this tool starts from PCoA coordinates and several random configurations (fixed seed, so results are reproducible), keeps the lowest-stress solution and reports how many starts reached it — the more, the more likely it is the global optimum.
Computation is heavier, so press “Run” after changing settings. Ellipses only describe within-group spread; test group differences with PERMANOVA / ANOSIM.
Kruskal J. B. (1964) Psychometrika 29:1–27 and 115–129; de Leeuw (1977) SMACOF; Clarke (1993) Aust J Ecol 18:117–143. Stress-1 uses the primary approach to ties and can be recomputed independently from the Shepard data; differences from scikit-learn non-metric MDS come from the random starts, and on the example data the stress here is no higher than its multi-start result + 0.01.
Up to 1,500 samples (several hundred samples take seconds to tens of seconds).
Send us your data and research question and you will receive a written plan within 1 working day: analysis steps, parameter rationale, deliverables and timeline. Quoted per project.