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Cluster analysis and mathematical programming
 Mathematical Programming
, 1997
"... Les textes publiés dans la série des rapports de recherche HEC n’engagent que la responsabilite ́ de leurs auteurs. La publication de ces rapports de recherche bénéficie d’une subvention du Fonds F.C.A.R. ..."
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Cited by 92 (9 self)
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Les textes publiés dans la série des rapports de recherche HEC n’engagent que la responsabilite ́ de leurs auteurs. La publication de ces rapports de recherche bénéficie d’une subvention du Fonds F.C.A.R.
The history of the cluster heat map
 The American Statistician
, 2009
"... 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 (column ..."
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Cited by 24 (0 self)
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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 there 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 we trace a diverse 20th century statistical literature that provided a foundation for this most widely used of all bioinformatics displays. 1
Rearrangement clustering: Pitfalls, remedies, and applications
 Journal of Machine Learning Research
, 2006
"... Given a matrix of values in which the rows correspond to objects and the columns correspond to features of the objects, rearrangement clustering is the problem of rearranging the rows of the matrix such that the sum of the similarities between adjacent rows is maximized. Referred to by various names ..."
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Cited by 9 (0 self)
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Given a matrix of values in which the rows correspond to objects and the columns correspond to features of the objects, rearrangement clustering is the problem of rearranging the rows of the matrix such that the sum of the similarities between adjacent rows is maximized. Referred to by various names and reinvented several times, this clustering technique has been extensively used in many fields over the last three decades. In this paper, we point out two critical pitfalls that have been previously overlooked. The first pitfall is deleterious when rearrangement clustering is applied to objects that form natural clusters. The second concerns a similarity metric that is commonly used. We present an algorithm that overcomes these pitfalls. This algorithm is based on a variation of the Traveling Salesman Problem. It offers an extra benefit as it automatically determines cluster boundaries. Using this algorithm, we optimally solve four benchmark problems and a 2,467gene expression data clustering problem. As expected, our new algorithm identifies better clusters than those found by previous approaches in all five cases. Overall, our results demonstrate the benefits of rectifying the pitfalls and exemplify the usefulness of this clustering technique. Our code is available at our websites.
History Corner The History of the Cluster Heat Map
"... 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 (colum ..."
Abstract
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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. KEY WORDS: Cluster analysis; Heatmap; Microarray; Visualization. 1.