Three Dissimilarity Measures to Contrast Dendrograms

Abstract

We discussed three dissimilarity measures between dendrograms defined over the same set, they are triples, partition, and cluster indices. All of them decompose the dendrograms into subsets. In the case of triples and partition indices, these subsets correspond to binary partitions containing some clusters, while in the cluster index, a novel dissimilarity method introduced in this paper, the subsets are exclusively clusters. In chemical applications, the dendrograms gather clusters that contain similarity information of the data set under study. Thereby, the cluster index is the most suitable dissimilarity measure between dendrograms resulting from chemical investigation. An application example of the three measures is shown to remark upon the advantages of the cluster index over the other two methods in similarity studies. Finally, the cluster index is used to measure the differences between five dendrograms obtained when applying five common hierarchical clustering algorithms on a database of 1000 molecules.

Structural‐Similarity‐Based Approaches for the Development of Clustering and QSPR/QSAR Models in Chemical Databases

“…This metric has been useful in chemical clustering applications for comparing results when different groups of descriptors or different similarity coefficients are used. In [88], three different indices for calculating dissimilarities and for analyzing different structural aspects between hierarchical clustering trees are described.…”

Algorithms for Computing Cluster Dissimilarity between Rooted Phylogenetic Trees

“…Tree comparison is very useful in querying databases of phylogenetic information [13]. Tree comparison is also used for other purposes, e.g., to assess the stability of the reconstruction algorithms [14], and in the comparative analysis of other hierarchical cluster structures [15,16].…”

On a matching distance between rooted phylogenetic trees

“…Moreover, a relatively new application concerns using polynomially computable tree comparison metrics in constructing heuristic algorithms for detecting Horizontal Gene Transfers (HGTs) (for details, see Boc et al, 2010). Phylogenetic tree distances are also useful in different branches of science, e.g., computer science-analysis of malware evolution (Hayes et al, 2009), chemistry (Restrepo et al, 2007) or linguistics Pompei et al, 2011).…”