Article

# Tree-Tree Matrices and other Combinatorial Problems from Taxonomy

06/1995; DOI:10.1006/eujc.1996.0017
Source: DBLP

ABSTRACT Let A be a bipartite graph between two sets D and T. Then A defines by Hamming distance, metrics on both T and D. The question is studied which pairs of metric spaces can arise this way. If both spaces are trivial the matrix A comes from a Hadamard matrix or is a BIBD. The second question studied is in what ways A can be used to transfer (classification) information from one of the two sets to the other. These problems find their origin in mathematical taxonomy. Mathematics subject classification 1991: 05B20, 05B25, 05C05, 54E35, 62H30, 68T10 Key words & phrases: bipartite graph, Hamming distance, tree metric space, tree, mathematical taxonomy, design, BIBD, generalized projective space, Hausdorff distance, Urysohn distance, Lipshits distance, cocitation analysis, clustering, ultrametric, single link clustering, linked design, balanced design 1.

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