Minimum Spanning Trees and Single Linkage Cluster Analysis

Gower, J. C.; Ross, G. J.

doi:10.2307/2346439

Cited by 1,016 publications

(542 citation statements)

References 10 publications

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“…Better results can be derived in a few cases: finding the M ST of G, ranking its edges by non-decreasing values and merging entities at endpoints of successive edges yields a θ(N 2 ) implementation of the single-linkage algorithm [50]. At each iteration, clusters correspond to connected components of a graph with the same vertex set as G and as edges those of M ST considered.…”

Section: Agglomerative Hierarchical Clustering Algorithmsmentioning

confidence: 99%

Cluster analysis and mathematical programming

Hansen

Jaumard

1997

Mathematical Programming

413

251

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Les textes publiés dans la série des rapports de recherche HEC n'engagent que la responsabilité de leurs auteurs. La publication de ces rapports de recherche bénéficie d'une subvention du Fonds F.C.A.R. Cluster Analysis and Mathematical ProgrammingPierre Hansen GERAD andÉcole des HautesÉtudes Commerciales Montréal, CanadaBrigitte Jaumard GERAD andÉcole Polytechnique de Montréal Canada February, 1997Les Cahiers du GERAD G-97-10Abstract Given a set of entities, Cluster Analysis aims at finding subsets, called clusters, which are homogeneous and/or well separated. As many types of clustering and criteria for homogeneity or separation are of interest, this is a vast field. A survey is given from a mathematical programming viewpoint.Steps of a clustering study, types of clustering and criteria are discussed. Then algorithms for hierarchical, partitioning, sequential, and additive clustering are studied. Emphasis is on solution methods, i.e., dynamic programming, graph theoretical algorithms, branch-and-bound, cutting planes, column generation and heuristics.

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Section: Agglomerative Hierarchical Clustering Algorithmsmentioning

confidence: 99%

Cluster analysis and mathematical programming

Hansen

Jaumard

1997

Mathematical Programming

413

251

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“…We compared ITM to the popular k-Means algorithm [14,13], to the MeanNN algorithm of Faivishevsky and Goldberger [5] and to single-link agglomerative clustering [8]. The similarities between single-link agglomerative clustering and the proposed MST-based optimization make it a good baseline for tree-based clustering approaches.…”

Section: Methodsmentioning

confidence: 99%

“…One of the earliest methods is single-link agglomerative clustering [8]. Single-link agglomerative clustering can be understood as a minimum spanning tree-based approach in which the largest edge is removed until the desired number of components is reached.…”

Section: Related Workmentioning

confidence: 99%

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Information Theoretic Clustering Using Minimum Spanning Trees

Müller

Nowozin

Lampert

2012

Lecture Notes in Computer Science

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Abstract. In this work we propose a new information-theoretic clustering algorithm that infers cluster memberships by direct optimization of a non-parametric mutual information estimate between data distribution and cluster assignment. Although the optimization objective has a solid theoretical foundation it is hard to optimize. We propose an approximate optimization formulation that leads to an efficient algorithm with low runtime complexity. The algorithm has a single free parameter, the number of clusters to find. We demonstrate superior performance on several synthetic and real datasets.

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“…We cluster the triplet fragments using the singlelinkage algorithm. 29 The procedures go as follows: for two triplets ( i , j ) and ( k , l ) under the criteria: D kl ij Ͻ D 0 , and i k and j l, the triplets will be clustered in the same group. Let G 1 and G 2 be two cluster groups, the former containing ( i , j ) and ( k , l ), the latter containing ( iЈ , jЈ ).…”

Section: Triplet Clusteringmentioning

confidence: 99%

The fragment transformation method to detect the protein structural motifs

Lin

Chen

et al. 2006

Proteins

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To identify functional structural motifs from protein structures of unknown function becomes increasingly important in recent years due to the progress of the structural genomics initiatives. Although certain structural patterns such as the Asp-His-Ser catalytic triad are easy to detect because of their conserved residues and stringently constrained geometry, it is usually more challenging to detect a general structural motifs like, for example, the ␤␤␣-metal binding motif, which has a much more variable conformation and sequence. At present, the identification of these motifs usually relies on manual procedures based on different structure and sequence analysis tools. In this study, we develop a structural alignment algorithm combining both structural and sequence information to identify the local structure motifs. We applied our method to the following examples: the ␤␤␣-metal binding motif and the treble clef motif. The ␤␤␣-metal binding motif plays an important role in nonspecific DNA interactions and cleavage in host defense and apoptosis. The treble clef motif is a zinc-binding motif adaptable to diverse functions such as the binding of nucleic acid and hydrolysis of phosphodiester bonds. Our results are encouraging, indicating that we can effectively identify these structural motifs in an automatic fashion. Our method may provide a useful means for automatic functional annotation through detecting structural motifs associated with particular functions. Proteins 2006;63:636 -643.

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Minimum Spanning Trees and Single Linkage Cluster Analysis

Cited by 1,016 publications

References 10 publications

Cluster analysis and mathematical programming

Cluster analysis and mathematical programming

Information Theoretic Clustering Using Minimum Spanning Trees

The fragment transformation method to detect the protein structural motifs

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