Clustering before or after ordination

Question

Can someone explain the implications of performing clustering either before or after performing NMDS?

I have some ecological data and I am performing a clustering analysis to identify communities of species which are more prevalent in certain samples.

I have thus far tried two approaches:

1) Perform NMDS on the raw data using vegan function metaMDS() with bray curtis dissimilarity and then cluster the ordination points and visualise.

2) First calculate the bray curtis dissimilarity matrix from the raw data and then perform clustering. Next I perform NMDS on the raw data and then visualise the clustering.

Both of these approaches yield approximately the same clustering however approach (1) performs better in context of silhouette width and gives a slightly better clustering (visually).

What are the implications of clustering before or after ordinations?

Answer 1

I always thought that no.1 was the appropriate way to run the NMDS w/ bray curtis. I don't understand why you would run it the 2nd way. One thing you could do to better compare the two would be to evaluate the stress of both approaches. Also when you run metamds the argument to autotransform is True so your raw data might be transformed regardless of how you input the data into the metaMDS function. I also believe that since you are using bay curtis dissimilarity as a distance in multivariate space to differentiate your sites in method 1, that should be sufficient and appropriate compared to your second method which to me seems redundant

Answer 2

The problem with running the NMDS first is that this loses information. There's no guarantee whatsoever that the information that doesn't show up in the NMDS results is irrelevant for clustering. If you can find an appropriate clustering directly on the dissimilarities, that'd be better.

That said, I have seen datasets that caused trouble for dissimilarity-based methods, and mixture model-based clustering after ordination worked better, probably because dissimilarities could be interpreted well compatible with the data as generated by some latent variables with Gaussian-shaped clusters.

Note by the way that it is not an argument in favour of clustering after ordination that the clusters look better on the NMDS output, because obviously you should expect that clustering the NMDS output is better at clustering the NMDS output (if you know what I mean;-). If the dissimilarity-based clustering has some strong influence of information not manifest in the NMDS, obviously the NMDS cannot show in which sense this is better. The Silhouette Width argument is more valid, because it means that the ordination-based clustering is also better in a dissimilarity-based sense.