contains the same information as the minimum method of hierarchical clustering and.For a given dissimilarity matrix, W, the PFnet(W, r, q) (2006) Interlink (1990) Schvaneveldt et al. There are some useful theoretical results for the Pathfinder algorithm (Schvaneveldt (1990) Guerrero-Bote et al. The structure (R+, ©, oo, 0) is a complete semiring with a* = 0. In the transformed space, the largest side of a triangle can be eliminated. Therefore, let d be a dissimilarity and for x, y, and z we have d(x, z) + d(z, y) > d(x, y) and d(x, y) > max(c/(x, z), c/(z, y)) then there exists a unique number p > 0 such that for all r > p The Pathfinder approach can be based on a Joly and Le Calve theorem (Joly and Le Calve 1986): For any even dissimilarity measure d there is a unique number p > 0, called its metric index, such that: dr is metric for all r p.įigure 3.11 A second example of a network and its Pathfinder skeleton.įigure 3.12 A display of World Trade 1999 network.įigure 3.13 Pathfinder skeleton of World Trade 1999 network. One version of this algorithm is expressed as: These skeletons show the essential connective structure of the two networks. The same holds for the World Trade 1999 network in Figure 3.12 and its PF skeleton in Figure 3.13. The results of applying the Pathfinder algorithm is shown on the right of this figure. In contrast, the networks on the left of Figure 3.11 are not. The network on the left of Figure 3.10 is completely readable.
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