An Interactive Multiobjective Programming Approach to Combinatorial Data Analysis

Abstract

combinatorial optimization, multiobjective programming, seriation,

Identifying a Reordering of Rows and Columns for Multiple Proximity Matrices Using Multiobjective Programming

“…For problems that are too large for dynamic programming, the multi-operation local search procedure developed by Hubert and Arabie (1994) is highly recommended. Although optimal solutions to the multiobjective programming problem are not guaranteed when this heuristic is used, computational evidence suggests that it performs very well (see Brusco & Stahl, 2001).…”

“…Consistent with Brusco and Stahl (2001), dynamic programming is the recommended solution procedure for providing an optimal solution to the multiobjective programming problem when computationally feasible. An excellent coverage of the dynamic programming paradigm for seriation and other combinatorial data analysis problems is provided by Hubert et al (2001).…”

“…Many approaches for fitting a structure to a single proximity matrix (with rows and columns corresponding to the same set of objects) require the identification of a reordering (or permutation) of the rows and columns of the matrix that optimizes some type of index Brusco & Stahl, 2001;Hubert, 1976Hubert, , 1978Hubert & Golledge, 1981b;Hubert & Schultz, 1976;Hubert, Arabie, & Meulman, 2001). Such problems are inherently combinatorial in nature and can frequently be described within the context of some broader framework, such as the quadratic assignment paradigm (Hubert & Schultz, 1976;Hubert et al, 2001).…”

“…In this regard, the problem can be viewed as an extension of a recent multiobjective programming approach to combinatorial data analysis (Brusco & Stahl, 2001). The key difference is that, whereas Brusco and Stahl were concerned with identification of a permutation for a single proximity matrix that provided good values for multiple structural indices, the focus herein is on finding a permutation for multiple proximity matrices each with their own relevant structural index.…”

Exploratory Approaches to Seriation by Asymmetric Multidimensional Scaling

“…Hubert and Golledge 1981, Hubert et al 2001, Brusco andStahl 2001), some authors (e.g. Rodgers and Thompson 1992) argued that it can profitably interact with multidimensional scaling (MDS) in the analysis of asymmetric proximity matrices, for reasons such as MDS could add meaningful information regarding dependencies between objects.…”