# What to use, k-means or hierarchical clustering for presence absence data?

I am currently working with a presence-absence database that is mostly zeros (~5% are ones) representing species in space (a species per site matrix). I would like to explore the spatial pattern of the species and see whether there is any "natural" grouping of the data that could be thought of as bioregions. I have been explored different clustering methods (hierarchical clustering and kmeans) using two different metrics [Hellingher distance and $Bsim=a/a+(min(b,c))$; where $a$ is the shared species between two sites and $b$ an $c$ are the unique species for each site].

There is also another variation doing multidimensional scaling over the distance matrix, before running the kmeans cluster. My thinking is that by reducing everything to two or three dimensions (am working with up to 600 species), this would limit the "freedom" of the centroids to move around all the dimensions as every new pixel is added. The counter argument is that it will render the solution more stable and avoid error propagation.

While it is possible to do some kind of validation of the final clusters (e.g., represent the clusters in a map and relate their borders to some topographic or any other environmental feature), I would like to know: How can I decide between the different clustering methods and distance metrics? What are the pros and cons in terms of mathematics or statistics?

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See also (stats.stackexchange.com/questions/27323/…) for similar question. – Miroslav Sabo Oct 9 '12 at 16:41
Welcome to the site. You don't need to add your name at the end, the program does it automatically. I also used LaTeX on your formula – Peter Flom Oct 9 '12 at 20:06
I noticed an anonymous edit on your post: For kmeans+Hellinger dist the data are pretransformed by $\sqrt(Y_{ij}/Y_{i+})$ so when kmeans calculates euclidean distance is actually calculating Hellingers'. Have you lost your account information? (The present account is already registered.) – chl Oct 10 '12 at 18:36