Cases of Doubt in Allocation Problems

Habbema, J. D. F.; Hermans, J.; Burgt, A. T. van der

doi:10.2307/2334360

Cited by 11 publications

(14 citation statements)

References 5 publications

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“…Methods developed for two-group constrained discrimination include a ranking procedure introduced by Broffitt et al (1976) and enhanced by Beckman and Johnson (2006). Habbema et al (1974) introduce a twogroup decision-theoretic method. Lee and Wu provide a comprehensive summary of mathematical programming approaches for classification (Lee and Wu 2007).…”

Section: Introductionmentioning

confidence: 99%

Analysis of the consistency of a mixed integer programming-based multi-category constrained discriminant model

Brooks

Lee

2008

Ann Oper Res

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Classification is concerned with the development of rules for the allocation of observations to groups, and is a fundamental problem in machine learning. Much of previous work on classification models investigates two-group discrimination. Multi-category classification is less-often considered due to the tendency of generalizations of two-group models to produce misclassification rates that are higher than desirable. Indeed, producing "good" two-group classification rules is a challenging task for some applications, and producing good multi-category rules is generally more difficult. Additionally, even when the "optimal" classification rule is known, inter-group misclassification rates may be higher than tolerable for a given classification model. We investigate properties of a mixed-integer programming based multi-category classification model that allows for the pre-specification of limits on inter-group misclassification rates. The mechanism by which the limits are satisfied is the use of a reserved judgment region, an artificial category into which observations are placed whose attributes do not sufficiently indicate membership to any particular group. The method is shown to be a consistent estimator of a classification rule with misclassification limits, and performance on simulated and real-world data is demonstrated.

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Section: Introductionmentioning

confidence: 99%

Analysis of the consistency of a mixed integer programming-based multi-category constrained discriminant model

Brooks

Lee

2008

Ann Oper Res

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“…The use of plain kernel density estimators has been shown to work well in a wide variety of real-world discrimination problems (see Habbema et al, 1974;Michie et al, 1994;Hall et al, 1995;Wright et al, 1995). Nevertheless, we note that in kernel-based classification problems we are not primarily interested in density estimation per se, but as a route to classification.…”

Section: Introductionmentioning

confidence: 99%

Kernel density classification and boosting: an L2 analysis

Marzio

Taylor

2005

Stat Comput

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University of LeedsAbstract. Kernel density estimation is a commonly used approach to classification. However, most of the theoretical results for kernel methods apply to estimation per se and not necessarily to classification. In this paper we show that when estimating the difference between two densities, the optimal smoothing parameters are increasing functions of the sample size of the complementary group, and we provide a small simluation study which examines the relative performance of kernel density methods when the final goal is classification.A relative newcomer to the classification portfolio is "boosting", and this paper proposes an algorithm for boosting kernel density classifiers. We note that boosting is closely linked to a previously proposed method of bias reduction in kernel density estimation and indicate how it will enjoy similar properties for classification. We show that boosting kernel classifiers reduces the bias whilst only slightly increasing the variance, with an overall reduction in error. Numerical examples and simulations are used to illustrate the findings, and we also suggest further areas of research.

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“…Therefore, using the features selected here, it is possible to differentiate the majority of metaphases from garbage. 1. Names and meanings of the tested features: global cluster features ( 1 4 , global cluster object features (7)(8)(9)(10)(11) and features of sized objects within the cluster (12-13. metaphases classified as garbage. Further differentiation of the metaphases into prometaphases, usable metaphases and unusable metaphases appears, however, to be much less reliable.…”

Section: Analysis Of the Feature Datamentioning

confidence: 99%

“…sible to make more refined analysis by considering classification with doubt matrices (8). In this procedure a cell is classified if the highest probability exceeds a certain preset level.…”

Section: Classification With Doubt: Using This Program It Is Pos-mentioning

confidence: 99%

Automated selection of metaphase cells by quality,

Berg¹,

Habbema

Raatgever³

1981

Cytometry

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The performance of metaphase-finding systems could be improved if they were able to determine the quality of the cells detected. This paper discusses the extent to which this may be realized by the introduction of a metaphase-quality parameter. Data obtained from 300 cells were statistically analyzed. Seventeen features were measured and nine visual properties were determined for each cell. Discriminant analysis and regression analysis were used to extract those features and visual properties which contribute to assessment of metaphase quality. Rather low correlations were found beIn the early 1970s several groups worked on systems for automated chromosome analysis (2, 3, 10, 12, 13). At f i s t , the ambitious aim was to develop fully automatic analysis systems; later an approach with operator-interaction seemed to be more appropriate. However, interest became focussed more and more on automating the localization of metaphase cells on the microscope slide. It was thought that, in a two-step approach, a system should first be able to search in a fully automatic way for suitable cells and store their slide coordinates, and that later, in a semiautomatic mode, the cells which had been located would be quickly recalled one by one and examined as to their suitability for further analysis (4,5,7, 13, 20, 21).Until now, most of the systems developed for automated metaphase selection have been designed to be fast enough to meet arbitrary criteria for an acceptable operating speed. It appears that, for many researchers, operating speed was a more important factor than the quality of the found metaphases.The importance of determining the quality of the automatically selected cells is mentioned in previous publications, and such an approach is seen as a promising way to improve the ' Presented at Automated Cytology VIT, Asilomar, California, November 25-30,1979, Supported by "Praeventiefonds", Grant 2826411.tween the selected measured features and visual properties. A quality-parameter based on a linear combination of cluster projections, areas and perimeters was found to account for 64% of the variation between visual and measured quality indicators. In addition, an increase in the predictive value for finding usable metaphases from 2 8 4 8 % was achieved.

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Cases of Doubt in Allocation Problems

Cited by 11 publications

References 5 publications

Analysis of the consistency of a mixed integer programming-based multi-category constrained discriminant model

Analysis of the consistency of a mixed integer programming-based multi-category constrained discriminant model

Kernel density classification and boosting: an L2 analysis

Automated selection of metaphase cells by quality,

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