This paper focuses on the clustering of leaf-labelled trees on free leafset. It extends the previously proposed algorithms, designed for trees on the same leafset. The term z-equality is proposed and all the necessary consensus and distance notions are redefined with respect to z-equality. The clustering algorithms that focus on maximizing the quality measure for two representative trees are described, together with the measure itself. Finally, the promising results of experiments on tandem duplication trees are presented.
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