Compact integer-programming models for extracting subsets of stimuli from confusion matrices

Brusco, Michael J.; Stahl, Stephanie

doi:10.1007/bf02294442

Cited by 13 publications

(19 citation statements)

References 44 publications

(69 reference statements)

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“…At this point, we believe that quantitative psychologists should be cautious in their optimism concerning the utility of integer linear programming for seriation and other problems in combinatorial data analysis. Nevertheless, the results presented herein, along with those recently obtained by Brusco and Stahl (2001b) for problems concerned with extracting subsets of stimuli from confusion matrices, reveal that integer linear programming is capable of providing optimal solutions for certain types of practically sized problems in quantitative psychology. It is hoped that the success of these recent implementations will stimulate the development and testing of integer linear programming models for related problems.…”

Section: Discussionmentioning

confidence: 55%

Seriation of asymmetric matrices using integer linear programming

Brusco

2001

Brit J Math & Statis

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Integer linear programming approaches for seriation of asymmetric n x n proximity matrices have generally been perceived as intractable for problems of practical size. However, to date, no computational evidence has been provided regarding the effectiveness (or ineffectiveness) of such approaches. This paper presents an evaluation of an integer linear programming method for asymmetric seriation using five moderately sized matrices (15 < or = n < or = 36) from the psychological literature, as well as 80 synthetic matrices (20 < or = n < or = 30). The solution to the linear programming relaxation of the integer-programming model was integer-optimal for each of the five empirical matrices and many of the synthetic matrices. In such instances, branch-and-bound integer programming was not required and optimal orderings were obtained within a few seconds. In all cases where the solution to the linear programming relaxation was not integer-optimal, branch-and-bound integer programming was able to find an optimal seriation in 18 minutes or less. A pragmatic solution strategy for larger matrices (n > 30) is also presented. This approach exploits the fact that, in many instances, only a modest percentage of all possible transitivity constraints are required to obtain an optimal solution.

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Section: Discussionmentioning

confidence: 55%

Seriation of asymmetric matrices using integer linear programming

Brusco

2001

Brit J Math & Statis

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“…Brusco and Stahl () described integer programming approaches for subset selection problems for which the objective functions were based on the sum of proximity elements both within and between subsets. In their models, both the number of subsets and the number of items per subset were prespecified as constraints.…”

Section: Discussionmentioning

confidence: 99%

“…Subset selection problems occur in applications that are specifically relevant to the psychological sciences, such as recognition/confusion studies and test construction. Brusco and Stahl (), Brusco and Steinley (), and Heiser () have described methods for subset selection problems pertaining to the extraction of a subset of stimulus objects from a larger set of stimuli in confusion experiments. Applications related to confusion experiments include the selection of a subset of letters as priming signals for feedback (Derryberry, ), the selection of letter subsets to serve as analogue stressors in a study of arousal and coping propensity (Lees & Neufeld, ), and the selection of a subset of automotive control signals for ergonomic design (Theise, ).…”

Section: Introductionmentioning

confidence: 99%

An evaluation of exact methods for the multiple subset maximum cardinality selection problem

Brusco

Köhn

Steinley

2016

Brit J Math & Statis

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The maximum cardinality subset selection problem requires finding the largest possible subset from a set of objects, such that one or more conditions are satisfied. An important extension of this problem is to extract multiple subsets, where the addition of one more object to a larger subset would always be preferred to increases in the size of one or more smaller subsets. We refer to this as the multiple subset maximum cardinality selection problem (MSMCSP). A recently published branch-and-bound algorithm solves the MSMCSP as a partitioning problem. Unfortunately, the computational requirement associated with the algorithm is often enormous, thus rendering the method infeasible from a practical standpoint. In this paper, we present an alternative approach that successively solves a series of binary integer linear programs to obtain a globally optimal solution to the MSMCSP. Computational comparisons of the methods using published similarity data for 45 food items reveal that the proposed sequential method is computationally far more efficient than the branch-and-bound approach.

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“…Constraint set (5) requires that each y ijkl variable assumes a value of one if x ik and x jk are both equal to one. Accordingly, the y ijkl variables provide a linearization of the quadratic term x ik x jk , which is a strategy that has also been used for integer programming models developed for the quadratic assignment problem (Kaufman & Broeckx, 1978; Lawler, 1963) and subset extraction (Brusco & Stahl, 2001; Theise, 1989). Some of the constraints in set (5) are superfluous and can be eliminated because i = j ⇒ k = l in the one-mode blockmodeling context.…”

Section: A Formulation For One-mode Blockmodeling Based On Structumentioning

confidence: 99%

Integer programs for one- and two-mode blockmodeling based on prespecified image matrices for structural and regular equivalence

Brusco¹,

Steinley²

2009

Journal of Mathematical Psychology

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Establishing blockmodels for one- and two-mode binary network matrices has typically been accomplished using multiple restarts of heuristic algorithms that minimize functions of inconsistency with ideal block structure. Although these algorithms likely yield exceptional performance, they are not assured to provide blockmodels that optimize the functional indices. In this paper, we present integer programming models that, for a prespecified image matrix, can produce guaranteed optimal solutions for matrices of nontrivial size. Accordingly, analysts performing a confirmatory analysis of a prespecified blockmodel structure can apply our models directly to obtain an optimal solution. In exploratory cases where a blockmodel structure is not prespecified, we recommend a two-stage procedure, where a heuristic method is first used to identify an image matrix and the integer program is subsequently formulated and solved to identify the optimal solution for that image matrix. Although best suited for ideal block structures associated with structural equivalence, the integer programming models have the flexibility to accommodate functional indices pertaining to regular equivalence. Computational results are reported for a variety of one- and two-mode matrices from the blockmodeling literature.

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Compact integer-programming models for extracting subsets of stimuli from confusion matrices

Abstract: combinatorial data analysis, confusion matrix, integer programming,

Cited by 13 publications

References 44 publications

Seriation of asymmetric matrices using integer linear programming

Seriation of asymmetric matrices using integer linear programming

An evaluation of exact methods for the multiple subset maximum cardinality selection problem

Integer programs for one- and two-mode blockmodeling based on prespecified image matrices for structural and regular equivalence

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