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                <term xml:lang="en">Apresjan hierarchy</term>
                <term xml:lang="en">Hierarchical Agglomerative Clustering</term>
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                <term xml:lang="en">Apresjan hierarchy Hierarchical Agglomerative Clustering Linkage function</term>
                <term xml:lang="en">Apresjan hierarchy</term>
                <term xml:lang="en">Apresjan hierarchy</term>
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              <p>The model of an Apresjan cluster is a formal account of what the intuitive notion of cluster amounts to. The set of all Apresjan clusters forms a hierarchy, called the Apresjan hierarchy. In this note, we identify a general class of linkage functions for which the Hierarchical Agglomerative Clustering (HAC)  algorithm generates hierarchies containing the Apresjan hierarchy. We deduce that, if the HAC algorithm is applied with a standard linkage function not based on centroids, then every generated hierarchy contains the Apresjan hierarchy. We also present preliminary results related to the HAC algorithm and arbitrary linkage functions, e.g. the characterization of all subsets belonging to all hierarchies generated by the HAC algorithm when this algorithm is applied to a given dataset and used with an arbitrarily chosen linkage function.</p>
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