Abstract
The paper presents a methodology for classifying three-way dissimilarity data, which are reconstructed by a small number of consensus classifications of the objects each defined by a sum of two order constrained distance matrices, so as to identify both a partition and an indexed hierarchy.
Specifically, the dissimilarity matrices are partitioned in homogeneous classes and, within each class, a partition and an indexed hierarchy are simultaneously fitted.
The model proposed is mathematically formalized as a constrained mixed-integer quadratic problem to be fitted in the least-squares sense and an alternating least-squares algorithm is proposed which is computationally efficient.
Two applications of the methodology are also described together with an extensive simulation to investigate the performance of the algorithm.
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Vicari, D., Vichi, M. Structural Classification Analysis of Three-Way Dissimilarity Data. J Classif 26, 121–154 (2009). https://doi.org/10.1007/s00357-009-9033-0
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DOI: https://doi.org/10.1007/s00357-009-9033-0