Graph theoretic foundations of pathfinder networks

AbstractThis paper is primarily expository, relating elements of graph theory to a computational theory of psychological similarity (or dissimilarity). A class of networks called Pathfinder networks (PFNETs) is defined. PFNETs are derived from estimates of dissimilarity for pairs of entities. Thus, PFNETs can be used to reveal aspects of the structure inherent in a set of pairwise estimates of dissimilarity. In order to accommodate different assumptions about the nature of the measurement scale (i.e. ordinal, interval, ratio) underlying the data, the Minkowski r-metric (also known as the L norm) is adapted to computing distances in networks. PFNETs are derived from data by: (1) regarding the matrix of dissimilarities as a network adjacency matrix (the DATANET); (2) computing the distance matrix (or r-distance matrix using the Minkowski r-metric) of the DATANET and (3) reducing the DATANET by eliminating each arc that has weight greater than the r-distance between the nodes connected by the arc. PFNET properties of inclusion, relation to minimal spanning trees, and invariance under transformations of data are discussed