Abstract
Order-constrained dissimilarity matrices (e.g., Robinson, strongly-Robinson, ultrametric matrices) are generally used as clustering models to fit the best hierarchical classification to the observed dissimilarity matrix, by minimizing a loss function, e.g. the least-squares criterion. Generally, a similar strategy has not being directly considered for non-hierarchical cluster analysis. In this paper such classifications are represented as order-constrained distance matrices with at most two off-main diagonal positive entries. Several bijections between non-hierarchical clustering structures and order-constrained distance matrices are established.
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References
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Vicari, D., Vichi, M. (2000). Non-Hierarchical Classification Structures. In: Gaul, W., Opitz, O., Schader, M. (eds) Data Analysis. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58250-9_5
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DOI: https://doi.org/10.1007/978-3-642-58250-9_5
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