Abstract
It is customary to split clustering analysis into an optimization level, then a (preferably) graphical representation level to take benefit of human vision for an effective understanding of (big) data structure. This article aspires to clarify relationships between clustering, both its process and its representation, and the underlying structural graph properties, both algebraic and geometric, starting from the mere knowledge of a dissimilarity matrix among items, possibly with missing entries. It is inspired by an analogous work on seriation problem, relating Robinson property in a dissimilarity with missing entries, with interval graph recognition using a sequence of 4 lexicographic breadth first searches.
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All problems have been solved using CPLEX under IBM Academic Initiative
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An anonymous referee deeply interacts with the manuscript so that it brings many clarifications and improvements. The author is grateful to him/her for the deep and accurate reviewing.
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Fortin, D. Clustering Analysis of a Dissimilarity: a Review of Algebraic and Geometric Representation. J Classif 37, 180–202 (2020). https://doi.org/10.1007/s00357-019-09315-7
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DOI: https://doi.org/10.1007/s00357-019-09315-7