NMDS

Non-metric multidimensional scaling (NMDS) is an ordination technique used to visualize the similarity structure of multivariate data. Unlike metric multidimensional scaling, NMDS is rank-based and makes few assumptions about the data’s distribution or linear relationships, making it popular in ecology, microbiology, and other fields dealing with complex community data.

NMDS begins with a matrix of pairwise dissimilarities among samples, computed with a distance measure suited to the data (for example Bray-Curtis for abundance data, Jaccard for presence–absence, or UniFrac for phylogenetic information). The method seeks a configuration of samples in a low-dimensional space (typically two or three dimensions) such that the rank order of the distances between points reflects the rank order of the original dissimilarities. Iterative optimization, often using the SMACOF algorithm, adjusts coordinates to minimize a stress function that quantifies mismatch between the original dissimilarities and the distances in the reduced space, applying a monotone transformation of dissimilarities as part of the process.

The resulting plot conveys relative similarity: points that cluster together are more similar in composition than distant points. The axes in an NMDS plot have no inherent meaning; interpretation focuses on patterns, groupings, and gradients. Model fit is summarized by a stress value, with lower values indicating better fit; common guidelines place stress below 0.1 as good, though context matters. Researchers may also inspect Shepard plots or perform multiple random starts to assess stability and avoid local minima.

NMDS is often complemented by statistical tests and fitting procedures, such as PERMANOVA to test for group differences or envfit to project environmental variables onto the ordination. It is implemented in software including R’s vegan package (metaMDS), and in non-metric MDS options within Python's scikit-learn and MATLAB toolboxes.