Ebook: Trees and Hierarchical Structures: Proceedings of a Conference held at Bielefeld, FRG, Oct. 5–9th, 1987

The "raison d'etre" of hierarchical dustering theory stems from one basic phe­ nomenon: This is the notorious non-transitivity of similarity relations. In spite of the fact that very often two objects may be quite similar to a third without being that similar to each other, one still wants to dassify objects according to their similarity. This should be achieved by grouping them into a hierarchy of non-overlapping dusters such that any two objects in ~ne duster appear to be more related to each other than they are to objects outside this duster. In everyday life, as well as in essentially every field of scientific investigation, there is an urge to reduce complexity by recognizing and establishing reasonable das­ sification schemes. Unfortunately, this is counterbalanced by the experience of seemingly unavoidable deadlocks caused by the existence of sequences of objects, each comparatively similar to the next, but the last rather different from the first.

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The notorious non-transitivity of similarity relations is the main problem encountered when - as in taxonomic studies in biology - one wants to base classification schemes on observed similarities and dissimilarities. While recent advances in molecular biology give rise to impressive new and rather abstract data structures which can easily be used as input for automatic classification procedures we are still very much in need of a better and deeper understanding of the many delicate points which need consideration once (semi-)automatic classification procedures are applied to biological or other data. The papers collected in this volume are devoted to precisely this problem. They study various theoretical aspects of three reconstruction methods in biology, and psychology, discuss their value in specific biological contexts, apply tree-like recursion networks in chess programming and indicate a conceptual framework for studying cluster analysis from a purely mathematical point of view.

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The notorious non-transitivity of similarity relations is the main problem encountered when - as in taxonomic studies in biology - one wants to base classification schemes on observed similarities and dissimilarities. While recent advances in molecular biology give rise to impressive new and rather abstract data structures which can easily be used as input for automatic classification procedures we are still very much in need of a better and deeper understanding of the many delicate points which need consideration once (semi-)automatic classification procedures are applied to biological or other data. The papers collected in this volume are devoted to precisely this problem. They study various theoretical aspects of three reconstruction methods in biology, and psychology, discuss their value in specific biological contexts, apply tree-like recursion networks in chess programming and indicate a conceptual framework for studying cluster analysis from a purely mathematical point of view.
Content:
Front Matter....Pages ii-v
Introduction....Pages 1-7
Reconstruction of Phylogenies by Distance Data: Mathematical Framework and Statistical Analysis....Pages 9-42
Additive-Tree Representations....Pages 43-59
Finding the Minimal Change in a Given Tree....Pages 60-74
Search, Parallelism, Comparison, and Evaluation: Algorithms for Evolutionary Trees....Pages 75-91
The Phylogeny of Prochloron: Is There Numerical Evidence from S AB Values? A Response to Van Valen....Pages 92-99
Evolution of the Collagen Fibril by Duplication and Diversification of a Small Primordial Exon Unit....Pages 100-116
The Poincare Paradox and the Cluster Problem....Pages 117-124
An Incremental Error Correcting Evaluation Algorithm For Recursion Networks without Circuits....Pages 125-137
Back Matter....Pages 139-141

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The notorious non-transitivity of similarity relations is the main problem encountered when - as in taxonomic studies in biology - one wants to base classification schemes on observed similarities and dissimilarities. While recent advances in molecular biology give rise to impressive new and rather abstract data structures which can easily be used as input for automatic classification procedures we are still very much in need of a better and deeper understanding of the many delicate points which need consideration once (semi-)automatic classification procedures are applied to biological or other data. The papers collected in this volume are devoted to precisely this problem. They study various theoretical aspects of three reconstruction methods in biology, and psychology, discuss their value in specific biological contexts, apply tree-like recursion networks in chess programming and indicate a conceptual framework for studying cluster analysis from a purely mathematical point of view.
Content:
Front Matter....Pages ii-v
Introduction....Pages 1-7
Reconstruction of Phylogenies by Distance Data: Mathematical Framework and Statistical Analysis....Pages 9-42
Additive-Tree Representations....Pages 43-59
Finding the Minimal Change in a Given Tree....Pages 60-74
Search, Parallelism, Comparison, and Evaluation: Algorithms for Evolutionary Trees....Pages 75-91
The Phylogeny of Prochloron: Is There Numerical Evidence from S AB Values? A Response to Van Valen....Pages 92-99
Evolution of the Collagen Fibril by Duplication and Diversification of a Small Primordial Exon Unit....Pages 100-116
The Poincare Paradox and the Cluster Problem....Pages 117-124
An Incremental Error Correcting Evaluation Algorithm For Recursion Networks without Circuits....Pages 125-137
Back Matter....Pages 139-141
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