Graph theoretical representations of proximities by monotonic network analysis (MONA)
Proximity data can be represented either geometrically or graph theoretically. Graph theoretical methods, however, are typically restricted to representations in terms of trees. As an new method, monotonic network analysis (MONA) allows for more general representations of proximity data. For a given set of data, MONA yields a connected graph, weighted by positive integers and possessing a distance function in such a way that (1) the vertices represent the empirical objects, (2) the number of edges is minimal, (3) the weights are minimal, and (4) the ordering of the distances coincides at least approximately (according to some prescribed error criterion) with the ordering of the dissimilarities. The rationale of MONA will be stated, and the method will be illustrated by applications to real data.
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