Unclassed matrix shading and optimal ordering in hierarchical cluster analysis

Gale, Nathan; Halperin, William C.; Costanzo, C. Michael

doi:10.1007/bf01890117

Cited by 33 publications

(22 citation statements)

References 15 publications

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“…Matrix shading is an old technique to visualize clusterings by displaying the rearranged matrices (see, e.g., Sneath and Sokal 1973;Ling 1973;Gale, Halperin, and Costanzo 1984). Initially matrix shading was used in connection with hierarchical clustering, where the order of the dendrogram leaf nodes was used to arrange the matrix.…”

Section: Dissimilarity Plotmentioning

confidence: 99%

Getting Things in Order: An Introduction to theRPackageseriation

Hahsler¹,

Hornik²,

Buchta³

2008

J. Stat. Soft.

231

195

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Seriation, i.e., finding a suitable linear order for a set of objects given data and a loss or merit function, is a basic problem in data analysis. Caused by the problem's combinatorial nature, it is hard to solve for all but very small sets. Nevertheless, both exact solution methods and heuristics are available. In this paper we present the package seriation which provides an infrastructure for seriation with R. The infrastructure comprises data structures to represent linear orders as permutation vectors, a wide array of seriation methods using a consistent interface, a method to calculate the value of various loss and merit functions, and several visualization techniques which build on seriation. To illustrate how easily the package can be applied for a variety of applications, a comprehensive collection of examples is presented.

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Section: Dissimilarity Plotmentioning

confidence: 99%

Getting Things in Order: An Introduction to theRPackageseriation

Hahsler¹,

Hornik²,

Buchta³

2008

J. Stat. Soft.

231

195

View full text Add to dashboard Cite

show abstract

“…Gruvaeus and Wainer (1972) developed a greedy algorithm that Wilkinson used in the SYSTAT display. Gale, Halperin, and Costanzo (1984) devised an alternative algorithm for this purpose. More recent articles have discussed this problem in detail and specified optimization algorithms with objective functions designed for the task (Wishart 1997;Bar-joseph et al 2003;Morris, Asnake, and Yen 2003).…”

Section: Seriating a Binary Treementioning

confidence: 99%

The History of the Cluster Heat Map

Wilkinson

Friendly

2009

The American Statistician

703

346

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His t o r y Co r n e rThe Histor y of the Cluster Heat Map Leland WILKINSON and Michael FRIENDLY The cluster heat map is an ingenious display that simultaneously reveals row and column hierarchical cluster structure in a data matrix. It consists of a rectangular tiling, with each tile shaded on a color scale to represent the value of the corresponding element of the data matrix. The rows (columns) of the tiling are ordered such that similar rows (columns) are near each other. On the vertical and horizontal margins of the tiling are hierarchical cluster trees. This cluster heat map is a synthesis of several different graphic displays developed by statisticians over more than a century. We locate the earliest sources of this display in late 19th century publications, and trace a diverse 20th century statistical literature that provided a foundation for this most widely used of all bioinformatics displays.

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“…The visualization technique presented in this paper is based on a different technique called matrix shading (see, e.g., Sneath and Sokal, 1973;Ling, 1973;Gale, Halperin, and Costanzo, 1984). For matrix shading, each value in the matrix is represented by a square with the intensity of the color depending on the value.…”

Section: Introductionmentioning

confidence: 99%

Dissimilarity Plots: A Visual Exploration Tool for Partitional Clustering

Hahsler

Hornik

2011

Journal of Computational and Graphical Statistics

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For hierarchical clustering, dendrograms provide convenient and powerful visualization. Although many visualization methods have been suggested for partitional clustering, their usefulness deteriorates quickly with increasing dimensionality of the data and/or they fail to represent structure between and within clusters simultaneously. In this paper we extend (dissimilarity) matrix shading with several reordering steps based on seriation. Both methods, matrix shading and seriation, have been well-known for a long time. However, only recent algorithmic improvements allow to use seriation for larger problems. Furthermore, seriation is used in a novel stepwise process (within each cluster and between clusters) which leads to a visualization technique that is independent of the dimensionality of the data. A big advantage is that it presents the structure between clusters and the micro-structure within clusters in one concise plot. This not only allows for judging cluster quality but also makes mis-specification of the number of clusters apparent. We give a detailed discussion of the construction of dissimilarity plots and demonstrate their usefulness with several examples.

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Unclassed matrix shading and optimal ordering in hierarchical cluster analysis

Abstract: Hierarchical clustering, Choropleth mapping, Matrix reorganization, Unidimensional seriation, Ordered binary trees,

Cited by 33 publications

References 15 publications

Getting Things in Order: An Introduction to theRPackageseriation

Getting Things in Order: An Introduction to theRPackageseriation

The History of the Cluster Heat Map

Dissimilarity Plots: A Visual Exploration Tool for Partitional Clustering

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