What are the exact assumptions behind the use of UPGMA? Can I use a non-Euclidean metric? This may result in a non-Euclidean distance matrix. What kind of bias may I encounter if I do so? References are appreciated.
While you can modify any algorithm as you see fit, in its pure form UPGMA has the following underlying assumptions at work:
UPGMA (Unweighted Pair-Group Method with Averages), arithmetic average - the average distance between elements of each cluster (weighted by the number of elements).
For example, (AB) and C+(DE) = (55+3x45)/3 = 63.33
Additional Comparative Algorithmic Context
Below is a list of algorithms and their general framework as it relates to each algorithm:
SINGLE (Single-link method) – brings together the closest elements.
WPGMA (Weighted Pair-Group Method with Averages), arithmetic average (not weighted by the number of elements).
- WPGMC (Weighted Pair-Group Method with Centroid Average), centroid average (assumes dissimilarity).
- WPGMS (Weighted Pair-Group Method with Spearman Average), Spearman's average (assumes correlation).
Reference for Modifying UPGMA
The paper below is a wonderful resource for "what-if" scenarios as it relates to UPGMA: