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On the binary classification problem in discriminant analysis using linear programming methods

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OLUSOLA M. O., ONYEAGU S. I.

Operations Research and Decisions

2020

vol. 30

issue 1

119-130

This paper is centred on a binary classification problem in which it is desired to assign a new object with multivariate features to one of two distinct populations as based on historical sets of samples from two populations. A linear discriminant analysis framework has been proposed, called the minimised sum of deviations by proportion (MSDP) to model the binary classification problem. In the MSDP formulation, the sum of the proportion of exterior deviations is minimised subject to the group separation constraints, the normalisation constraint, the upper bound constraints on proportions of exterior deviations and the sign unrestriction vis-à-vis the non-negativity constraints. The two-phase method in linear programming is adopted as a solution technique to generate the discriminant function. The decision rule on group-membership prediction is constructed using the apparent error rate. The performance of the MSDP has been compared with some existing linear discriminant models using a previously published dataset on road casualties. The MSDP model was more promising and well suited for the imbalanced dataset on road casualties.

Prediction of a Function of Misclassified Binary Data

86%

Al-Kandari N. M.

Statistics in Transition new series

2016

vol. 17

issue 3

429-448

We consider the problem of predicting a function of misclassified binary variables. We make an interesting observation that the naive predictor, which ignores the misclassification errors, is unbiased even if the total misclassification error is high as long as the probabilities of false positives and false negatives are identical. Other than this case, the bias of the naive predictor depends on the misclassification distribution and the magnitude of the bias can be high in certain cases. We correct the bias of the naive predictor using a double sampling idea where both inaccurate and accurate measurements are taken on the binary variable for all the units of a sample drawn from the original data using a probability sampling scheme. Using this additional information and design-based sample survey theory, we derive a biascorrected predictor. We examine the cases where the new bias-corrected predictors can also improve over the naive predictor in terms of mean square error (MSE).

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1 Operations Research and Decisions

1 Statistics in Transition new series

1 Al-Kandari N. M.

1 OLUSOLA M. O.

1 ONYEAGU S. I.

1 2020

1 2016

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On the binary classification problem in discriminant analysis using linear programming methods

Prediction of a Function of Misclassified Binary Data