Heuristic Implementation of Dynamic Programming for Matrix Permutation Problems in Combinatorial Data Analysis

Brusco, Michael J.; Köhn, Hans Friedrich; Stahl, Stephanie

doi:10.1007/s11336-007-9049-5

Cited by 30 publications

(20 citation statements)

References 54 publications

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“…In Table 1 we summarize the methods currently available in the package for seriation. The code for the simulated annealing heuristic (Brusco, Köhn, and Stahl 2008) and the two branch-andbound implementations (Brusco and Stahl 2005) Chen (2002). Note that some methods implemented (e.g., the rank-two ellipse seriation) do not fall within the combinatorial optimization framework of this paper and thus are not dealt with here in detail.…”

Section: The Package Infrastructurementioning

confidence: 99%

Getting Things in Order: An Introduction to theRPackageseriation

Hahsler¹,

Hornik²,

Buchta³

2008

J. Stat. Soft.

233

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: The Package Infrastructurementioning

confidence: 99%

Getting Things in Order: An Introduction to theRPackageseriation

Hahsler¹,

Hornik²,

Buchta³

2008

J. Stat. Soft.

233

195

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“…Benati (2008) applies VNS to categorical data fuzzy clustering. Other clustering problem applications appear in Brusco et al (2008). Another important data mining task which has been managed with VNS is classification.…”

Section: Data Miningmentioning

confidence: 99%

Variable neighbourhood search: methods and applications

Hansen

Mladenović

Moreno-Pérez

2008

4OR

258

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Variable neighbourhood search (VNS) is a metaheuristic, or a framework for building heuristics, based upon systematic changes of neighbourhoods both in descent phase, to find a local minimum, and in perturbation phase to emerge from the corresponding valley. It was first proposed in 1997 and has since then rapidly developed both in its methods and its applications. In the present paper, these two aspects are thoroughly reviewed and an extensive bibliography is provided. Moreover, one section is devoted to newcomers. It consists of steps for developing a heuristic for any particular problem. Those steps are common to the implementation of other metaheuristics.

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“…For even larger problems heuristics can be employed. Recently a heuristic which combines dynamic programming with simulated annealing was developed by Brusco et al (2008). This heuristic produces very good average results and allows to find close to optimal solutions for much larger problems.…”

Section: Seriationmentioning

confidence: 99%

“…The seriation of clusters is done using branch-and-bound to find the optimal solution (Brusco and Stahl, 2005). For the seriation for all objects in each cluster we use a simulated annealing heuristic (Brusco et al, 2008). The implementation of both algorithms is provided by Michael Brusco and is available in the R extension package seriation (Hahsler, Buchta, and Hornik, 2009).…”

Section: Examplesmentioning

confidence: 99%

“…Seriation is a combinatorial problem and thus in general very difficult to solve for all but extremely small problems. Recently a very efficient algorithm for the seriation problem based on branchand-bound (Brusco and Stahl, 2005) and a heuristic that combines dynamic programming combined with simulated annealing (Brusco, Köhn, and Stahl, 2008) have been developed. This algorithmic progress allows us to use seriation for visualization of clusterings of larger data sets.…”

Section: Introductionmentioning

confidence: 99%

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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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Heuristic Implementation of Dynamic Programming for Matrix Permutation Problems in Combinatorial Data Analysis

Abstract: Combinatorial data analysis, matrix permutation, dynamic programming, heuristics,

Cited by 30 publications

References 54 publications

Getting Things in Order: An Introduction to theRPackageseriation

Getting Things in Order: An Introduction to theRPackageseriation

Variable neighbourhood search: methods and applications

Dissimilarity Plots: A Visual Exploration Tool for Partitional Clustering

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