A quite known clustering technique, Single linkage, can be considered an
example of the seriation procedure (actually, based on the minimum spanning
tree construction) leading to the global maximum of a corresponding "minimum
split" set function. The purpose of this work is to have the property
extended to a class of the linkage functions called monotone linkages.
It is proved that the monotone linkage functions are minimum split functions
for the quasi-convex set functions (and only for them). This allows to
prove that the global optima of the quasi-convex set functions can be found
with the multiple seriation algorithm based on corresponding linkage function.
Paper available at: ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1995/95-44.ps.gz